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Aurélien Benoit-Lévy University College London in collaboration with Gabriel Chardin Benoit-Lévy, Chardin, A&A, 537, A78, 2012 WAG 2013 - Bern - November 15th The Dirac-Milne Universe

The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

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Page 1: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

Aurélien Benoit-LévyUniversity College London

in collaboration with Gabriel ChardinBenoit-Lévy, Chardin, A&A, 537, A78, 2012

WAG 2013 - Bern - November 15th

The Dirac-Milne Universe

Page 2: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

The Dirac-Milne Universe

Aurélien Benoit-LévyUniversity College London

in collaboration with Gabriel ChardinBenoit-Lévy, Chardin, A&A, 537, A78, 2012

WAG 2013 - Bern - November 15th

a.k.a. What if antimatter falls up?

Page 3: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

Inflationary universe, dominated today by Dark matter and Dark Energy

2 10 500

1000

2000

3000

4000

5000

6000

D`[µK

2 ]

90� 18�

500 1000 1500 2000 2500

Multipole moment, `

1� 0.2� 0.1� 0.07�Angular scale

ΛCDM is a very good fit

Using Planck + WP, at 1-sigma:

•  Peak scale 0.060% BBN consistency:

•  Baryon density 1.3%

•  CDM density 2.3%

•  Primordial amplitude 2.5%

•  Primordial spectral index 0.76%

•  Reionization optical depth 0.13%

Derived (model-dependent) parameters:

•  Hubble parameter

•  Λ fractional density

•  Reionization redshift

25.03.2013 Planck implications for cosmology – J. Lesgourgues 25

Planck + WP

Agreement between data and theory over 3 decades of angular scale!

Standard model of cosmology

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

http://www.einstein.unibe.ch/WAG2013.html Contact: [email protected]

©!Bern!Tourism!

Page 4: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

Concordance model!

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

http://www.einstein.unibe.ch/WAG2013.html Contact: [email protected]

©!Bern!Tourism!

Page 5: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

95% of our Universe escapes our knowledge

Dark Matter

Baryon content from Standard Big-Bang nucleosynthesis not sufficient

Still escapes direct detection

Dark Energy

True cosmological constant: why this value?

Vacuum energy: 10120 times smaller than expected

"Coincidence problem "

Inflation

Introduced to solve horizon and flatness problem

Standard model relies on 3 ingredients which are undetected and /or not understood

So why looking for something else?

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

http://www.einstein.unibe.ch/WAG2013.html Contact: [email protected]

©!Bern!Tourism!

Page 6: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

Let’s get rid of Inflation, Dark Energy, and Dark Matter

but assume

Matter - antimatter symmetric Universe

Antimatter is supposed to have a negative active gravitational mass

The Dirac-Milne Universe

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

http://www.einstein.unibe.ch/WAG2013.html Contact: [email protected]

©!Bern!Tourism!

Page 7: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

then two connected by the annular singularity

Antimatter naturally comes as negative mass candidate from Kerr-Newman solution

In the second space, the solution is seen as having reversed charge and mass (Carter 68)

This strongly suggests antimatter!

Also implies that cannot create negative mass as independent degree of freedom

R4

(q, m, a)

(q, m, a) =��e,me,

⇥2

k = �1

(e, r, m)⇧ (�e,�m,�r)

a(t) ⌃ t

TCMB = 2.725 K

T⇤ = 1.94 K

p = ⇧⌅

�R = ...

�� ⇤ 0.72

�B ⇤ 0.04

�DM ⇤ 0.24

�M ⇤ ��

⇤ =�⇤ ⇥�

csd⇥

⇥ �sinh (ln(1 + z⇥))

1 + z⇥

⇥�1

t ⌃ T�1

t ⌃ T�2

t ⌃ T�3/2

a(t) ⌃ t�

� = 1

�b ⌅ 0.3

t0 =1

H0⌅ 13.9⇥ 109 years

⇤t =

⇧⌅2 � ⇤2

r = tanh�1 ⇤⌅

dh(t) = a(t)⌅ t

t0

dt⇤

a(t⇤)t0⇥0�⌅ +⌥

a > 0

Gµ⇥ = ⇥Tµ⇥

⌅ t0

0

dt

a(t)= +⌥

⇧2Dirac�Milne = ⇧2

�CDM

⇤ + 3p < 0

R4

(q, m,ma)

(q, m,ma) =��e,me,

⇥2

k = �1

(r, e, m)⇧ (�r,�e,�m)

a(t) ⌃ t

T⇥ = TCMB = 2.725 K

T⇥ = 1.94 K

p = ⌃⇤

�R ⇤ 8⇥ 10�5

�� ⇤ 0.72

�B ⇤ 0.04

�DM ⇤ 0.24

H�10

� ⇤ 8⇥ 10�9

When

⇤t =

⇧⌅2 � ⇤2

r = tanh�1 ⇤⌅

dh(t) = a(t)⌅ t

t0

dt⇤

a(t⇤)t0⇥0�⌅ +⌥

a > 0

Gµ⇥ = ⇥Tµ⇥

⌅ t0

0

dt

a(t)= +⌥

⇧2Dirac�Milne = ⇧2

�CDM

⇤ + 3p < 0

R4

(q, m,ma)

(q, m,ma) =��e,me,

⇥2

k = �1

(r, e, m)⇧ (�r,�e,�m)

a(t) ⌃ t

T⇥ = TCMB = 2.725 K

T⇥ = 1.94 K

p = ⌃⇤

�R ⇤ 8⇥ 10�5

�� ⇤ 0.72

�B ⇤ 0.04

�DM ⇤ 0.24

H�10

� ⇤ 8⇥ 10�9

Solution is symmetric under

Motivation for negative mass

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

http://www.einstein.unibe.ch/WAG2013.html Contact: [email protected]

©!Bern!Tourism!

Page 8: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

“Runaway” solution (Bondi 57)

If antimatter is Bondi-type negative mass, antihydrogen weighting experiments should see antimatter fall as matter

+- -

+ +

-

(and then the ideal would be to build a big clump of antimatter to study its own gravitational potential... )

Negative mass in GR

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

http://www.einstein.unibe.ch/WAG2013.html Contact: [email protected]

©!Bern!Tourism!

Page 9: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

9

A Bondi mass in Earth gravitational field

F

a

gF = 0

Positive and negative mass, linked by a string

Cut the string:Both particles fall

a

a

R. Price, Am. J. Phys, 61(3), 1993“Negative mass can be positively amusing”

Negative mass in GR

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

http://www.einstein.unibe.ch/WAG2013.html Contact: [email protected]

©!Bern!Tourism!

Page 10: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

Negative mass in GR

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

http://www.einstein.unibe.ch/WAG2013.html Contact: [email protected]

©!Bern!Tourism!

Could Bondi-type negative mass work in Cosmology?

Page 11: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

To have a viable cosmology, we need mutual repulsion between matter and antimatter

Negative mass in GR

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

http://www.einstein.unibe.ch/WAG2013.html Contact: [email protected]

©!Bern!Tourism!

Could Bondi-type negative mass work in Cosmology?

Page 12: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

Cosmological principle: Universe is homogeneous and isotropic

GM

c2R

ds2 = c2dt2 � a(t)2⌥

dr2

1� kr2+ r2

�d⌅2 + sin2 ⌅d�2

⇥�

ds2 = dt2 � a(t)2⇧

dr2

1� kr2+ r2d⇥2

Gµ⌅ = Rµ⌅ �12Rgµ⌅ = 8⌃GTµ⌅

Gµ⌅ = 8⌃GTµ⌅

cs =c⌦

3(1 + R), R =

3⌥b

4⌥�

�⌅EdS

�⌅Milne=

sinh(ln(1 + z))

2⇤1� 1⌅

1+z

⌅ =z=1100⇣ 284

�⌅�⌅

=2⇤1 = 1⌅

1+z

sinh(ln(1 + z))=

z=1100⇣ 0.00352⇤ 1.

⌅�CDM

⌅Milne=

dMilneA (z)

d�CDMA (z)

=z=1100⇣ 173

(z) = a0

a01+z

da

aaz⇥+⇤�⌅ +⇧

dL = f(z, cosmologie)

(z) z⇥+⇤�⌅ +⇧

µ = m� �M + �(s� 1)� ⇥c

rs = trec

0csd⇤ =

trec

0cs

dt

a(t)

rs = ⇥rec

0csd⇤ =

trec

0cs

dt

a(t)

⌅ =rs

dA

⌅Milne ⇥ 1.2

k: space curvaturea: scale factor

12

Friedman-Robertson-Lemaître-Walker metric

Some equations...

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

http://www.einstein.unibe.ch/WAG2013.html Contact: [email protected]

©!Bern!Tourism!

Page 13: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

Cosmological principle: Universe is homogeneous and isotropic

GM

c2R

ds2 = c2dt2 � a(t)2⌥

dr2

1� kr2+ r2

�d⌅2 + sin2 ⌅d�2

⇥�

ds2 = dt2 � a(t)2⇧

dr2

1� kr2+ r2d⇥2

Gµ⌅ = Rµ⌅ �12Rgµ⌅ = 8⌃GTµ⌅

Gµ⌅ = 8⌃GTµ⌅

cs =c⌦

3(1 + R), R =

3⌥b

4⌥�

�⌅EdS

�⌅Milne=

sinh(ln(1 + z))

2⇤1� 1⌅

1+z

⌅ =z=1100⇣ 284

�⌅�⌅

=2⇤1 = 1⌅

1+z

sinh(ln(1 + z))=

z=1100⇣ 0.00352⇤ 1.

⌅�CDM

⌅Milne=

dMilneA (z)

d�CDMA (z)

=z=1100⇣ 173

(z) = a0

a01+z

da

aaz⇥+⇤�⌅ +⇧

dL = f(z, cosmologie)

(z) z⇥+⇤�⌅ +⇧

µ = m� �M + �(s� 1)� ⇥c

rs = trec

0csd⇤ =

trec

0cs

dt

a(t)

rs = ⇥rec

0csd⇤ =

trec

0cs

dt

a(t)

⌅ =rs

dA

⌅Milne ⇥ 1.2

k: space curvaturea: scale factor

Einstein equation:

⇥ ⇥

⇥ ⇥•

⇥� ⇥�d1 d2

d3

d4

⇤⌅

Ci�1,j�1 Ci,j�1

Ci,jCi�1,j

GM

c2R

ds2 = c2dt2 � a(t)2⌥

dr2

1� kr2+ r2

�d�2 + sin2 �d⌅2

⇥�

ds2 = dt2 � a(t)2⇧

dr2

1� kr2+ r2d⇥2

Gµ⇤ = Rµ⇤ �12Rgµ⇤ = 8⇥GTµ⇤

Gµ⇤ = 8⇥G Tµ⇤

p

cs =c⌦

3(1 + R), R =

3⇤b

4⇤�

��EdS

��Milne=

sinh(ln(1 + z))

2⇤1� 1⌅

1+z

⌅ =z=1100

� 284

��

��=

2⇤1 = 1⌅

1+z

sinh(ln(1 + z))=

z=1100� 0.00352⌅ 1.

��CDM

�Milne=

dMilneA (z)

d�CDMA (z)

=z=1100

� 173

⇧(z) = a0

a01+z

da

aaz⇥+⇤�⇧ +⌃

13

Friedman-Robertson-Lemaître-Walker metric

Some equations...

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

http://www.einstein.unibe.ch/WAG2013.html Contact: [email protected]

©!Bern!Tourism!

Page 14: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

Cosmological principle: Universe is homogeneous and isotropic

GM

c2R

ds2 = c2dt2 � a(t)2⌥

dr2

1� kr2+ r2

�d⌅2 + sin2 ⌅d�2

⇥�

ds2 = dt2 � a(t)2⇧

dr2

1� kr2+ r2d⇥2

Gµ⌅ = Rµ⌅ �12Rgµ⌅ = 8⌃GTµ⌅

Gµ⌅ = 8⌃GTµ⌅

cs =c⌦

3(1 + R), R =

3⌥b

4⌥�

�⌅EdS

�⌅Milne=

sinh(ln(1 + z))

2⇤1� 1⌅

1+z

⌅ =z=1100⇣ 284

�⌅�⌅

=2⇤1 = 1⌅

1+z

sinh(ln(1 + z))=

z=1100⇣ 0.00352⇤ 1.

⌅�CDM

⌅Milne=

dMilneA (z)

d�CDMA (z)

=z=1100⇣ 173

(z) = a0

a01+z

da

aaz⇥+⇤�⌅ +⇧

dL = f(z, cosmologie)

(z) z⇥+⇤�⌅ +⇧

µ = m� �M + �(s� 1)� ⇥c

rs = trec

0csd⇤ =

trec

0cs

dt

a(t)

rs = ⇥rec

0csd⇤ =

trec

0cs

dt

a(t)

⌅ =rs

dA

⌅Milne ⇥ 1.2

k: space curvaturea: scale factor

Einstein equation:

⇥ ⇥

⇥ ⇥•

⇥� ⇥�d1 d2

d3

d4

⇤⌅

Ci�1,j�1 Ci,j�1

Ci,jCi�1,j

GM

c2R

ds2 = c2dt2 � a(t)2⌥

dr2

1� kr2+ r2

�d�2 + sin2 �d⌅2

⇥�

ds2 = dt2 � a(t)2⇧

dr2

1� kr2+ r2d⇥2

Gµ⇤ = Rµ⇤ �12Rgµ⇤ = 8⇥GTµ⇤

Gµ⇤ = 8⇥G Tµ⇤

p

cs =c⌦

3(1 + R), R =

3⇤b

4⇤�

��EdS

��Milne=

sinh(ln(1 + z))

2⇤1� 1⌅

1+z

⌅ =z=1100

� 284

��

��=

2⇤1 = 1⌅

1+z

sinh(ln(1 + z))=

z=1100� 0.00352⌅ 1.

��CDM

�Milne=

dMilneA (z)

d�CDMA (z)

=z=1100

� 173

⇧(z) = a0

a01+z

da

aaz⇥+⇤�⇧ +⌃

t0 =1

H0⇤ 13.9� 109 years

⇧a

a

⌃2

= H20

��M a�3 + �Ra�4 + �ka

�2 + ��⇥

⇧a

a

⌃2

= H20

⌥�M

⇤a0

a

⌅3+ �k

⇤a0

a

⌅2+ ��

⇧a

a

⌃2

= H20

⌥�M

⇤a0

a

⌅3+ �R

⇤a0

a

⌅4+ �k

⇤a0

a

⌅2+ ��

⇧a

a

⌃2

= H20

⇤a0

a

⌅2⇧ a(t) ⌃ t

e + � ⌅ e + �

e + � ⌅ e + � + �

e + N ⌅ e + N + �

�r = 0

t =1

H0

T0

T

p + e� ⌅ H + �

�M = 0

(= m)

a

k + a

t0 =1

H0⇥ 14� 109 ans, avec H0 = 70 km/s/Mpc

t0 =1

H0= 13.9� 109 ans

t0 =1

H0= 13, 9� 109 years,with H0 = 70 km/s/Mpc

a(t) = t

Friedmann equation: time evolution of expansion

Pressureless matter:Baryonic + non-

baryonic Radiation:Photon and neutrino background

Curvature:complementary term

Dark Energy:Cosmological constant, or?

14

Friedman-Robertson-Lemaître-Walker metric

Some equations...

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

http://www.einstein.unibe.ch/WAG2013.html Contact: [email protected]

©!Bern!Tourism!

Page 15: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

Cosmological principle: Universe is homogeneous and isotropic

GM

c2R

ds2 = c2dt2 � a(t)2⌥

dr2

1� kr2+ r2

�d⌅2 + sin2 ⌅d�2

⇥�

ds2 = dt2 � a(t)2⇧

dr2

1� kr2+ r2d⇥2

Gµ⌅ = Rµ⌅ �12Rgµ⌅ = 8⌃GTµ⌅

Gµ⌅ = 8⌃GTµ⌅

cs =c⌦

3(1 + R), R =

3⌥b

4⌥�

�⌅EdS

�⌅Milne=

sinh(ln(1 + z))

2⇤1� 1⌅

1+z

⌅ =z=1100⇣ 284

�⌅�⌅

=2⇤1 = 1⌅

1+z

sinh(ln(1 + z))=

z=1100⇣ 0.00352⇤ 1.

⌅�CDM

⌅Milne=

dMilneA (z)

d�CDMA (z)

=z=1100⇣ 173

(z) = a0

a01+z

da

aaz⇥+⇤�⌅ +⇧

dL = f(z, cosmologie)

(z) z⇥+⇤�⌅ +⇧

µ = m� �M + �(s� 1)� ⇥c

rs = trec

0csd⇤ =

trec

0cs

dt

a(t)

rs = ⇥rec

0csd⇤ =

trec

0cs

dt

a(t)

⌅ =rs

dA

⌅Milne ⇥ 1.2

k: space curvaturea: scale factor

Einstein equation:

⇥ ⇥

⇥ ⇥•

⇥� ⇥�d1 d2

d3

d4

⇤⌅

Ci�1,j�1 Ci,j�1

Ci,jCi�1,j

GM

c2R

ds2 = c2dt2 � a(t)2⌥

dr2

1� kr2+ r2

�d�2 + sin2 �d⌅2

⇥�

ds2 = dt2 � a(t)2⇧

dr2

1� kr2+ r2d⇥2

Gµ⇤ = Rµ⇤ �12Rgµ⇤ = 8⇥GTµ⇤

Gµ⇤ = 8⇥G Tµ⇤

p

cs =c⌦

3(1 + R), R =

3⇤b

4⇤�

��EdS

��Milne=

sinh(ln(1 + z))

2⇤1� 1⌅

1+z

⌅ =z=1100

� 284

��

��=

2⇤1 = 1⌅

1+z

sinh(ln(1 + z))=

z=1100� 0.00352⌅ 1.

��CDM

�Milne=

dMilneA (z)

d�CDMA (z)

=z=1100

� 173

⇧(z) = a0

a01+z

da

aaz⇥+⇤�⇧ +⌃

t0 =1

H0⇤ 13.9� 109 years

⇧a

a

⌃2

= H20

��M a�3 + �Ra�4 + �ka

�2 + ��⇥

⇧a

a

⌃2

= H20

⌥�M

⇤a0

a

⌅3+ �k

⇤a0

a

⌅2+ ��

⇧a

a

⌃2

= H20

⌥�M

⇤a0

a

⌅3+ �R

⇤a0

a

⌅4+ �k

⇤a0

a

⌅2+ ��

⇧a

a

⌃2

= H20

⇤a0

a

⌅2⇧ a(t) ⌃ t

e + � ⌅ e + �

e + � ⌅ e + � + �

e + N ⌅ e + N + �

�r = 0

t =1

H0

T0

T

p + e� ⌅ H + �

�M = 0

(= m)

a

k + a

t0 =1

H0⇥ 14� 109 ans, avec H0 = 70 km/s/Mpc

t0 =1

H0= 13.9� 109 ans

t0 =1

H0= 13, 9� 109 years,with H0 = 70 km/s/Mpc

a(t) = t

Friedmann equation: time evolution of expansion

~0.3 ~0 ~ 0.7

15

Friedman-Robertson-Lemaître-Walker metric

Some equations...

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

http://www.einstein.unibe.ch/WAG2013.html Contact: [email protected]

©!Bern!Tourism!

~ few 10-5LCDM

Page 16: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

Cosmological principle: Universe is homogeneous and isotropic

GM

c2R

ds2 = c2dt2 � a(t)2⌥

dr2

1� kr2+ r2

�d⌅2 + sin2 ⌅d�2

⇥�

ds2 = dt2 � a(t)2⇧

dr2

1� kr2+ r2d⇥2

Gµ⌅ = Rµ⌅ �12Rgµ⌅ = 8⌃GTµ⌅

Gµ⌅ = 8⌃GTµ⌅

cs =c⌦

3(1 + R), R =

3⌥b

4⌥�

�⌅EdS

�⌅Milne=

sinh(ln(1 + z))

2⇤1� 1⌅

1+z

⌅ =z=1100⇣ 284

�⌅�⌅

=2⇤1 = 1⌅

1+z

sinh(ln(1 + z))=

z=1100⇣ 0.00352⇤ 1.

⌅�CDM

⌅Milne=

dMilneA (z)

d�CDMA (z)

=z=1100⇣ 173

(z) = a0

a01+z

da

aaz⇥+⇤�⌅ +⇧

dL = f(z, cosmologie)

(z) z⇥+⇤�⌅ +⇧

µ = m� �M + �(s� 1)� ⇥c

rs = trec

0csd⇤ =

trec

0cs

dt

a(t)

rs = ⇥rec

0csd⇤ =

trec

0cs

dt

a(t)

⌅ =rs

dA

⌅Milne ⇥ 1.2

k: space curvaturea: scale factor

Einstein equation:

⇥ ⇥

⇥ ⇥•

⇥� ⇥�d1 d2

d3

d4

⇤⌅

Ci�1,j�1 Ci,j�1

Ci,jCi�1,j

GM

c2R

ds2 = c2dt2 � a(t)2⌥

dr2

1� kr2+ r2

�d�2 + sin2 �d⌅2

⇥�

ds2 = dt2 � a(t)2⇧

dr2

1� kr2+ r2d⇥2

Gµ⇤ = Rµ⇤ �12Rgµ⇤ = 8⇥GTµ⇤

Gµ⇤ = 8⇥G Tµ⇤

p

cs =c⌦

3(1 + R), R =

3⇤b

4⇤�

��EdS

��Milne=

sinh(ln(1 + z))

2⇤1� 1⌅

1+z

⌅ =z=1100

� 284

��

��=

2⇤1 = 1⌅

1+z

sinh(ln(1 + z))=

z=1100� 0.00352⌅ 1.

��CDM

�Milne=

dMilneA (z)

d�CDMA (z)

=z=1100

� 173

⇧(z) = a0

a01+z

da

aaz⇥+⇤�⇧ +⌃

t0 =1

H0⇤ 13.9� 109 years

⇧a

a

⌃2

= H20

��M a�3 + �Ra�4 + �ka

�2 + ��⇥

⇧a

a

⌃2

= H20

⌥�M

⇤a0

a

⌅3+ �k

⇤a0

a

⌅2+ ��

⇧a

a

⌃2

= H20

⌥�M

⇤a0

a

⌅3+ �R

⇤a0

a

⌅4+ �k

⇤a0

a

⌅2+ ��

⇧a

a

⌃2

= H20

⇤a0

a

⌅2⇧ a(t) ⌃ t

e + � ⌅ e + �

e + � ⌅ e + � + �

e + N ⌅ e + N + �

�r = 0

t =1

H0

T0

T

p + e� ⌅ H + �

�M = 0

(= m)

a

k + a

t0 =1

H0⇥ 14� 109 ans, avec H0 = 70 km/s/Mpc

t0 =1

H0= 13.9� 109 ans

t0 =1

H0= 13, 9� 109 years,with H0 = 70 km/s/Mpc

a(t) = t

Friedmann equation: time evolution of expansion

~0.3 ~0 ~ 0.7

16

Friedman-Robertson-Lemaître-Walker metric

Some equations...

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

http://www.einstein.unibe.ch/WAG2013.html Contact: [email protected]

©!Bern!Tourism!

~ few 10-5

0 1 00

LCDM

Dirac-Milne

Page 17: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

Flat space-time, open space

Tµ� = 0⇥⇤ a(t) = t and k = �1

C⇥⇤ = AC⇥

⇤ |fid

�PA = 0.061

�RA = 0.035

�PA =

(FCMB

AA )�1

�RA =

(F ⇥

AA)�1

FCMBAA =

⇧⇥CTT

⇥A

⌃2 1�CTT

⇤ + NTT⇤

⇥2

F ⇥AA =

⌥⇥C⇥⇥

⇥A

�21

⇤C⇥⇥

⇤ + N⇥⇥⇤

⌅2

Gradient : l1 + l2 + L and l3 + l4 + L even

Curl : l1 + l2 + L and l3 + l4 + L odd

T =T0

H0

1t

a2 + e2 + m2

4Rµ⌅⇥� = 0

a(t) = t

k = �1

ds2 = dt2 � t2dr2 � r2 sinh2 rd�2

ds2 = d⇤2 � d⇥2 � ⇥2d�2

t =⌅

⇤2 � ⇥2

r = tanh�1 ⇥

dh(t) = a(t)⇤ t

t0

dt⇤

a(t⇤)t0⇥0�⇥ +⇤

a > 0

Gµ⌅ = �Tµ⌅

⇤ t0

0

dt

a(t)= +⇤

⌅2Dirac�Milne = ⌅2

�CDM

⇥ + 3p < 0

R4

(q, m, a)

(q, m, a) =��e,me,

⇥2

k = �1

Standard Model Dirac-Milne Ratio

T= 170 MeV 3 x 10-5 sec 7 days 1.7 x 1010

T = 1 MeV 1 sec 3.3 yr 1 x 108

T = 80 keV ~200 sec 41 yr 6.5 x 106

T = 3000 K 380 000 yr 12 x 106 yr 32

T= T0 ~ H0-1 H0-1 ~ 1

Linear evolution with time of the scale factor

no acceleration (and no deceleration) of the expansion

a linear scale factor during the whole history of the Universe solves the horizon problem

No inflation needed to solve the horizon problem

No Dark Energy needed to solve the age problem

Some properties of the Dirac-Milne universe

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

http://www.einstein.unibe.ch/WAG2013.html Contact: [email protected]

©!Bern!Tourism!

µ = 1.4�U

U

⌃2/dof = 7.83

⌃2/dof = 7.30

⇥, e+e�

�m = 0.06 mag

p + p⇥ ⇥ + �⇥ D,3 He,3 H

p + �⇥ D,3 He,3 H

T =T0

H0

1t

a2 + e2 + m2

4Rµ⌅⇥� = 0

a(t) = t

k = �1

ds2 = dt2 � t2dr2 � r2 sinh2 rd⇥2

ds2 = d⇧2 � d⌅2 � ⌅2d⇥2

t =⇥

⇧2 � ⌅2

r = tanh�1 ⌅

dh(t) = a(t)� t

t0

dt⇤

a(t⇤)t0⇥0�⇥ +⇤

a > 0

Page 18: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

Thermal episode : production of 4He (Lohiya et al. 98 & Kaplinghat et al. 00) and 7Li

Late decoupling of weak reactions lead to 4He and 7Li

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

http://www.einstein.unibe.ch/WAG2013.html Contact: [email protected]

©!Bern!Tourism!

Big-Bang Nucleosynthesis

Page 19: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

Thermal episode : production of 4He (Lohiya et al. 98 & Kaplinghat et al. 00) and 7Li

Late decoupling of weak reactions lead to 4He and 7Li

No longer need for non-baryonic Dark Matter

102 Nucleosynthese

sont representes que les elements dont les abondances ne sont pas ridiculeusement faibles, et parsouci de clarte, j’ai choisi de decouper la figure en quatre. Sur chaque figure, j’ai egalement tracel’abondance de beryllium-7 (qui decroıt apres la recombinaison vers le lithium-7) afin d’etablirun point de comparaison. Ce qu’il ressort de cette figure, c’est que des quantites importantesd’azote-14, de neon-21 et de magnesium-25 sont produites durant la nucleosynthese de l’universde Dirac-Milne. Notons toutefois que le magnesium-25 est l’isotope stable le plus lourd inclusdans le code, et qu’ainsi son abondance represente en quelque sorte la somme des abondancesdes elements plus lourds non consideres dans le code. La raison de cette production importantede metaux est bien sur le temps passe a des temperatures assez elevees pour permettre auxreactions (p,⇥) et (p,�) de produire des elements lourds. Je n’ai pas juge utile d’inclure dansle code les reactions nucleaires permettant d’aller au dela du magnesium-25, car il n’y a pasd’observation des abondances primordiales des elements plus lourds que le lithium-7. Se posetoutefois la question de savoir si de telles quantites d’azote-14 peuvent etre mesurees et le casecheant comment s’assurer qu’il s’agit d’une mesure de l’abondance primordiale et non resultantd’un enrichissement en metaux par des explosions d’etoiles.

4.1.6 Influence de la densite baryonique

Comme dans le scenario standard, l’abondance des di�erents elements a la fin de la pro-duction thermique et homogene de la nucleosynthese ne depend que d’un seul parametre : ladensite baryonique. Cette densite est classiquement parametree par le rapport du nombre debaryons sur le nombre de photons, note ⇤. Nous avons vu dans le chapitre 1 que la valeur de cettegrandeur dans le cadre du modele standard etait proche de 6 � 10�10, qu’elle soit determineeen comparant les predictions de la nucleosynthese standard aux observations ou a partir desfluctuations de temperature du CMB. Dans l’univers de Dirac-Milne, on determine egalementla densite baryonique en comparant predictions de la nucleosynthese et observations. La com-paraison s’e�ectue en premier lieu grace a l’helium-4 puisque par nucleosynthese primordialeon entend principalement formation d’helium, les autres elements n’etant que des cendres pro-duites en proportion beaucoup plus faible . Ces cendres sont toutefois importantes puisqu’ellespermettent de confronter le scenario a ses predictions que ce soit dans le cas standard ou dansle cas de l’univers de Dirac-Milne.

La figure (4.4) presente les abondances en helium-4 et en lithium-7 (en realite le beryllium-7)en fonction de la densite baryonique. Les bandes horizontales representent les limites observa-tionnelles discutees dans le chapitre 1. Cette figure confirme l’a⌅rmation indiquee plus haut,a savoir que le mecanisme de nucleosynthese dans l’univers de Dirac-Milne permet e�ective-ment la production d’helium-4 et de lithium-7 a des niveaux comparables aux observations. Ladependance des abondances de ces deux elements vis-a-vis de la densite baryonique est forte.La densite baryonique qui permet d’obtenir une abondance d’helium-4 compatible avec les ob-servations se situe entre

8.8� 10�9 < ⇤ < 9.6� 10�9. (4.11)

On remarque que si l’on se fie aux barres d’erreurs des contraintes observationnelles sur lelithium-7, il n’y a pas de valeur de ⇤ qui donnerait une valeur compatible a la fois pour l’helium-4 et le lithium-7. Toutefois, la valeur minimale de ⇤ imposee par la contrainte sur l’helium-4

4.2 Nucleosynthese secondaire 105

fournit une abondance en lithium-7 de l’ordre de7LiH

= 3.45� 10�10. (4.12)

Cette valeur est certes plus grande que la valeur observationnelle consideree comme primor-diale, mais elle est legerement plus faible que la valeur predite par la nucleosynthese standard.C’est evidemment une pure coıncidence, mais le fait est que l’univers de Dirac-Milne produit dulithium-7 a une valeur comparable aux observations si la densite baryonique est telle que l’abon-dance d’helium-4 est, quant a elle, compatible avec les mesures d’helium. Ce point est assezremarquable car, si cela n’avait pas ete le cas, et que le lithium-7 avait ete produit dans l’universde Dirac-Milne a toute autre valeur, il aurait ete tres di⇤cile de trouver des scenarios permet-tant de produire ou detruire dans des proportions arbitraires ce lithium-7. Notons egalement quel’univers de Dirac-Milne ne resout pas le probleme du lithium-7. En e�et la valeur predite esttoujours plus grande que la valeur deduite des observations, mais la di�erence entre predictionet observations est moindre que dans le cas standard. Ainsi, le fait d’obtenir du lithium-7 par lescenario de nucleosynthese decrit dans cette partie ne constitue bien evidemment pas une preuvede la validite du modele mais assure neanmoins sa coherence sur ce point.

La figure (4.4) ne considere que ces deux elements car il n’en a pas pas d’autres qui seraientproduits par cette nucleosynthese thermique a des niveaux observes. En particulier, le deuteriumet helium-3 sont produits a des niveaux infinitesimaux (respectivement ⇥ 10�18 et ⇥ 10�13),largement inferieurs aux quelques 10�5 observes. Il convient maintenant d’etudier dans quellemesure la presence de domaines separes de matiere et d’antimatiere peut conduire a une produc-tion de ces deux elements et ainsi changer cette conclusion. C’est l’objet des parties suivantesdu chapitre.

Avant de passer a cette partie, il convient de revenir sur la densite baryonique necessaire pourobtenir une nucleosynthese de l’helium-4 satisfaisante. Cette densite baryonique est environ 15fois plus grande que celle habituellement consideree dans le modele standard. Ce point avait eteinitialement remarque dans [Lohiya et al. 1998]. Cette densite baryonique 15 fois plus grandeque celle du modele standard est une specificite du modele de Dirac-Milne. Elle signifie quetous les raisonnements e�ectues dans le cadre du modele standard qui reposent sur l’idee d’unedensite baryonique faible – en terme de densite critique, les baryons ne representent que 4%de l’Univers standard – sont a revoir dans le cadre du modele de Dirac-Milne. En particulierla necessite d’avoir une composante non-baryonique disparaıt. Cette necessite resultait du faitque dynamiquement, les galaxies et les amas de galaxies, ont besoin de plus de masse que nele permet des 4% de baryons habituellement consideres. Il etait donc necessaire d’invoquer lapresence d’une composante massive, mais qui ne serait pas composee de matiere baryonique.Avec une densite baryonique 15 fois plus importante cette conclusion ne tient plus, et il seranecessaire de considerer les mesures de masses en ayant en tete que, dans l’univers de Dirac-Milne, il y a 15 fois plus de baryons. Evidemment, ces baryons ne sont pas detectes autrementque par des mesures dynamiques et ce point sera discute dans le chapitre 6.

4.2 Nucleosynthese secondaire

Nous venons de voir dans quelles conditions il est possible, dans un univers evoluant avecun facteur d’echelle lineaire pendant l’epoque de la nucleosynthese primordiale, de produire de

Big-Bang Nucleosynthesis

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

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Page 20: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

Riess et al. 98 & Perlmutter et al. 99 discovered that distant SN Ia are dimmer than expected

Historical discovery of acceleration of expansion

Interpretation that the expansion is accelerating under the effect of Dark EnergyConfirmed by other experiments (e.g. SNLS)won 2011 Nobel prize

Type Ia Supernovae

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

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Page 21: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

Riess et al. 98 & Perlmutter et al. 99 discovered that distant SN Ia are dimmer than expected

Historical discovery of acceleration of expansion

Interpretation that the expansion is accelerating under the effect of Dark EnergyConfirmed by other experiments (e.g. SNLS)won 2011 Nobel prize

ButDirac-Mi lne universe does not present acceleration (nor deceleration) of the expansion

Nearby SN Ia are crucial

Dirac-Milne universe close to best-fit

(Astier et al. 06)SNLS data

RedshiftR

esid

uals

of H

ubbl

e di

agra

m

With only high-z SNe Ia, Dirac-Milne is as good as ΛCDM.

Type Ia Supernovae

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

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Page 22: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

Dirac-Milne universe close to best-fit

Type Ia Supernovae

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

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Page 23: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

observer

Photon Pressure

Effective Mass

Potential Well

Infall

last scattering surface

z=1000 recombinatione¾l-1

h¾k-1

Potential well sourced by Dark Matter

CMB and BAO?

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

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Before recombination: Acoustic oscillation in the baryons-photon fluid

164 Autres tests cosmologiques

6.1.3 Position du premier pic acoustique dans le cadre de l’univers de Dirac-Milne

L’echelle angulaire du premier pic acoustique (eq. (6.7)) fait intervenir deux quantites, ladistance angulaire et l’horizon sonore, dont les origines sont di�erentes. La distance angulaire estun terme purement geometrique et ainsi depend largement de la courbure des sections spatiales.Aussi, la position du premier pic a l’echelle angulaire du degre est classiquement interpreteecomme la preuve que l’espace dans lequel nous evoluons est plat.

Le calcul de la distance angulaire dans l’univers de Dirac-Milne a partir de l’equation (6.6)est immediat et donne

dA(z) = H�10

11 + z

sinh(ln(1 + z)). (6.10)

Le rapport des distances angulaires calculees pour le Modele de Concordance et l’univers deDirac-Milne au meme redshift donne le rapport des angles sous lesquels on verrait un memeobjet. Si l’on reprend les parametres utilises auparavant pour le modele de Concordance, ilvient :

dMilneA (z)

d�CDMA (z)

z=1100⌃ 163. (6.11)

Ce rapport signifie qu’a priori, on devrait voir le premier pic acoustique dans le cadre de l’universde Dirac-Milne a un angle environ 160 plus petit que dans le cadre du modele de Concordance.Autrement dit, si cela etait vrai, cela poserait une contrainte probablement insurmontable al’univers de Dirac-Milne. En realite, cet argument est incomplet car l’expression de l’horizonsonore change egalement de facon importante dans l’univers de Dirac-Milne.

L’horizon sonore s’exprime comme la distance maximale que peut parcourir une onde sepropageant a la vitesse du son jusqu’a la recombinaison. Rappelons son expression :

rs =⇥ t

0cs

dt⇥

a(t⇥). (6.12)

Considerons dans un premier temps que les baryons ne modifient que faiblement la vitesse duson, qui, dans un milieu constitue en premiere approximation d’un gaz de photons est egalea cs = 1/

�3. L’horizon sonore est alors, a un facteur constant pres, egal a l’horizon. Dans le

cadre de l’univers de Dirac-Milne, cette expression pour l’horizon sonore n’a pas de sens, carl’integrale diverge pres de sa borne inferieure. Il est ainsi necessaire de determiner a partir dequel moment et jusqu’a quand, des ondes acoustiques peuvent se former et se propager dansl’emulsion matiere-antimatiere. Une propagation d’ondes qui commencerait a partir du momentou l’emulsion apparaıt, vers 40 MeV (voir section 2.4.2), semble naturelle. De meme, il estlegitime de supposer que la propagation des ondes va s’arreter au moment du decouplage gravi-tationnel qui voit la separation entre les domaines de matiere de masse positive et d’antimatierede masse negative. Les contraintes de nucleosynthese, determinees au chapitre 4 indiquent unetemperature approximative de 7 eV. Le calcul de la position du pic acoustique dans l’universde Dirac-Milne peut donc se faire en calculant l’horizon sonore entre ces deux bornes. Il vientalors :

lA = �H0

� zini

zfincs

dz1+z

sinh(ln(1 + zdec)), (6.13)

This defines a characteristic length: the sound horizon

Page 24: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

First peak corresponds to acoustic scale given by sound horizon seen on last scattering surface.

dL = f(z, cosmologie)

⌃(z) z⌅+⇧�⌅ +⇧

µ = m⇥ �M + �(s� 1)� ⇥c

µ = m�M + �(s� 1)� ⇥ c

rs =� trec

0csd⇤ =

� trec

0cs

dt

a(t)

rs =� �rec

0csd⇤ =

� trec

0cs

dt

a(t)

⌅ =rs

dA

⌅Milne ⇤ 1.2

⌅Milne ⇤ 1.2⇤

rs =� trec

0cs

dt

a(t)

rs =� �rec

�0

csdt

a(t)

rs =� trec

t170MeV

csdt

a(t)

rs =�

csdt

a(t)

⌅Milne

⌅�CDM= 2.05

�b

�b ⇤ 4 10�2

⇤ ⇤ 3 10�10

⇤ ⇤ 6 10�10

⇤ ⇤ 7⇥ 10�9

⇤ ⇤ 8⇥ 10�9

2 10 500

1000

2000

3000

4000

5000

6000

D`[µK

2 ]

90� 18�

500 1000 1500 2000 2500

Multipole moment, `

1� 0.2� 0.1� 0.07�Angular scale

CMB and BAO?

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

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z~ 1100

z=0.57

Same things happens in galaxy distribution: BAO

Planck 2013

BOSS 2012

Page 25: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

164 Autres tests cosmologiques

6.1.3 Position du premier pic acoustique dans le cadre de l’univers de Dirac-Milne

L’echelle angulaire du premier pic acoustique (eq. (6.7)) fait intervenir deux quantites, ladistance angulaire et l’horizon sonore, dont les origines sont di�erentes. La distance angulaire estun terme purement geometrique et ainsi depend largement de la courbure des sections spatiales.Aussi, la position du premier pic a l’echelle angulaire du degre est classiquement interpreteecomme la preuve que l’espace dans lequel nous evoluons est plat.

Le calcul de la distance angulaire dans l’univers de Dirac-Milne a partir de l’equation (6.6)est immediat et donne

dA(z) = H�10

11 + z

sinh(ln(1 + z)). (6.10)

Le rapport des distances angulaires calculees pour le Modele de Concordance et l’univers deDirac-Milne au meme redshift donne le rapport des angles sous lesquels on verrait un memeobjet. Si l’on reprend les parametres utilises auparavant pour le modele de Concordance, ilvient :

dMilneA (z)

d�CDMA (z)

z=1100⌃ 163. (6.11)

Ce rapport signifie qu’a priori, on devrait voir le premier pic acoustique dans le cadre de l’universde Dirac-Milne a un angle environ 160 plus petit que dans le cadre du modele de Concordance.Autrement dit, si cela etait vrai, cela poserait une contrainte probablement insurmontable al’univers de Dirac-Milne. En realite, cet argument est incomplet car l’expression de l’horizonsonore change egalement de facon importante dans l’univers de Dirac-Milne.

L’horizon sonore s’exprime comme la distance maximale que peut parcourir une onde sepropageant a la vitesse du son jusqu’a la recombinaison. Rappelons son expression :

rs =⇥ t

0cs

dt⇥

a(t⇥). (6.12)

Considerons dans un premier temps que les baryons ne modifient que faiblement la vitesse duson, qui, dans un milieu constitue en premiere approximation d’un gaz de photons est egalea cs = 1/

�3. L’horizon sonore est alors, a un facteur constant pres, egal a l’horizon. Dans le

cadre de l’univers de Dirac-Milne, cette expression pour l’horizon sonore n’a pas de sens, carl’integrale diverge pres de sa borne inferieure. Il est ainsi necessaire de determiner a partir dequel moment et jusqu’a quand, des ondes acoustiques peuvent se former et se propager dansl’emulsion matiere-antimatiere. Une propagation d’ondes qui commencerait a partir du momentou l’emulsion apparaıt, vers 40 MeV (voir section 2.4.2), semble naturelle. De meme, il estlegitime de supposer que la propagation des ondes va s’arreter au moment du decouplage gravi-tationnel qui voit la separation entre les domaines de matiere de masse positive et d’antimatierede masse negative. Les contraintes de nucleosynthese, determinees au chapitre 4 indiquent unetemperature approximative de 7 eV. Le calcul de la position du pic acoustique dans l’universde Dirac-Milne peut donc se faire en calculant l’horizon sonore entre ces deux bornes. Il vientalors :

lA = �H0

� zini

zfincs

dz1+z

sinh(ln(1 + zdec)), (6.13)

For Dirac-Milne, angular distance

is 163 times larger than in ΛCDM.

one would expect a tiny angle!

But, due to linear scale factor, sound horizon is much larger than in standard model

164 Autres tests cosmologiques

6.1.3 Position du premier pic acoustique dans le cadre de l’univers de Dirac-Milne

L’echelle angulaire du premier pic acoustique (eq. (6.7)) fait intervenir deux quantites, ladistance angulaire et l’horizon sonore, dont les origines sont di�erentes. La distance angulaire estun terme purement geometrique et ainsi depend largement de la courbure des sections spatiales.Aussi, la position du premier pic a l’echelle angulaire du degre est classiquement interpreteecomme la preuve que l’espace dans lequel nous evoluons est plat.

Le calcul de la distance angulaire dans l’univers de Dirac-Milne a partir de l’equation (6.6)est immediat et donne

dA(z) = H�10

11 + z

sinh(ln(1 + z)). (6.10)

Le rapport des distances angulaires calculees pour le Modele de Concordance et l’univers deDirac-Milne au meme redshift donne le rapport des angles sous lesquels on verrait un memeobjet. Si l’on reprend les parametres utilises auparavant pour le modele de Concordance, ilvient :

dMilneA (z)

d�CDMA (z)

z=1100⌃ 163. (6.11)

Ce rapport signifie qu’a priori, on devrait voir le premier pic acoustique dans le cadre de l’universde Dirac-Milne a un angle environ 160 plus petit que dans le cadre du modele de Concordance.Autrement dit, si cela etait vrai, cela poserait une contrainte probablement insurmontable al’univers de Dirac-Milne. En realite, cet argument est incomplet car l’expression de l’horizonsonore change egalement de facon importante dans l’univers de Dirac-Milne.

L’horizon sonore s’exprime comme la distance maximale que peut parcourir une onde sepropageant a la vitesse du son jusqu’a la recombinaison. Rappelons son expression :

rs =⇥ t

0cs

dt⇥

a(t⇥). (6.12)

Considerons dans un premier temps que les baryons ne modifient que faiblement la vitesse duson, qui, dans un milieu constitue en premiere approximation d’un gaz de photons est egalea cs = 1/

�3. L’horizon sonore est alors, a un facteur constant pres, egal a l’horizon. Dans le

cadre de l’univers de Dirac-Milne, cette expression pour l’horizon sonore n’a pas de sens, carl’integrale diverge pres de sa borne inferieure. Il est ainsi necessaire de determiner a partir dequel moment et jusqu’a quand, des ondes acoustiques peuvent se former et se propager dansl’emulsion matiere-antimatiere. Une propagation d’ondes qui commencerait a partir du momentou l’emulsion apparaıt, vers 40 MeV (voir section 2.4.2), semble naturelle. De meme, il estlegitime de supposer que la propagation des ondes va s’arreter au moment du decouplage gravi-tationnel qui voit la separation entre les domaines de matiere de masse positive et d’antimatierede masse negative. Les contraintes de nucleosynthese, determinees au chapitre 4 indiquent unetemperature approximative de 7 eV. Le calcul de la position du pic acoustique dans l’universde Dirac-Milne peut donc se faire en calculant l’horizon sonore entre ces deux bornes. Il vientalors :

lA = �H0

� zini

zfincs

dz1+z

sinh(ln(1 + zdec)), (6.13)

Integrating from 40 MeV to ~7 eV (end of annihilation, cf BBN) yields acoustic scale around 1º !

Acoustic scale naturally emerges at 1º

CMB and BAO?

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

http://www.einstein.unibe.ch/WAG2013.html Contact: [email protected]

©!Bern!Tourism!

But then BAO can’t have the same explanation!

dL = f(z, cosmologie)

⌃(z) z⌅+⇧�⌅ +⇧

µ = m⇥ �M + �(s� 1)� ⇥c

µ = m�M + �(s� 1)� ⇥ c

rs =� trec

0csd⇤ =

� trec

0cs

dt

a(t)

rs =� �rec

0csd⇤ =

� trec

0cs

dt

a(t)

⌅ =rs

dA

⌅Milne ⇤ 1.2

⌅Milne ⇤ 1.2⇤

rs =� trec

0cs

dt

a(t)

rs =� �rec

�0

csdt

a(t)

rs =� trec

t170MeV

csdt

a(t)

rs =�

csdt

a(t)

⌅Milne

⌅�CDM= 2.05

�b

�b ⇤ 4 10�2

⇤ ⇤ 3 10�10

⇤ ⇤ 6 10�10

⇤ ⇤ 7⇥ 10�9

⇤ ⇤ 8⇥ 10�9

Page 26: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

Does Cosmology need alternative models?No, all the data is consistent with LCDM to a very good extent

Conclusion

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

http://www.einstein.unibe.ch/WAG2013.html Contact: [email protected]

©!Bern!Tourism!

Yes, we don’t know what’s CDM, and we really don’t know what’s L

Page 27: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

Does Cosmology need alternative models?No, all the data is consistent with LCDM to a very good extent

Conclusion

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

http://www.einstein.unibe.ch/WAG2013.html Contact: [email protected]

©!Bern!Tourism!

Yes, we don’t know what’s CDM, and we really don’t know what’s L

Is the Dirac-Milne a possible viable alternative cosmology?

No, it’s way too different to work...But BBN and SN Ia are not too far Still faces major theoretical and modelling issues

Page 28: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

Does Cosmology need alternative models?No, all the data is consistent with LCDM to a very good extent

Conclusion

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

http://www.einstein.unibe.ch/WAG2013.html Contact: [email protected]

©!Bern!Tourism!

Yes, we don’t know what’s CDM, and we really don’t know what’s L

Is the Dirac-Milne a possible viable alternative cosmology?

No, it’s way too different to work...But BBN and SN Ia are not too far Still faces major theoretical and modelling issues

How “gbar” experiments will help?

Antimatter falls up: at least we have a cosmological model to start with ...Antimatter falls down: at least we can rule out something!

Page 29: The Dirac-Milne Universe · 2018. 11. 15. · The Dirac-Milne Universe 2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013 Albert Einstein

Late decoupling of weak reactions, lead to 4He and 7Li

D and 3He are totally destroyed by this thermal process

Domain size ~7 kpc comoving,but size at the moment of production. Will evolve after recombination

3He/D >> 1, possibly a constraint as 3He/D is observed <1 (Sigl et al. 95)

Thermal episode : production of 4He and 7Li (Lohiya et al. 98 & Kaplinghat et al. 00, ABL & Chardin 12)

BBN compatible with D, 4He, 7Litension with 3He

Annihilation at the border of domains

D and 3He final abundances as function of the typical size of domains

Annihilation at the border of domains

p + p⇥ ⇥ + �⇥ D,3 He,3 H

p + �⇥ D,3 He,3 H

T =T0

H0

1t

a2 + e2 + m2

4Rµ⌅⇥� = 0

a(t) = t

k = �1

ds2 = dt2 � t2dr2 � r2 sinh2 rd�2

ds2 = d⇧2 � d⌅2 � ⌅2d�2

t =⇥

⇧2 � ⌅2

r = tanh�1 ⌅

dh(t) = a(t)� t

t0

dt⇤

a(t⇤)t0⇥0�⇥ +⇤

a > 0

Gµ⌅ = ⇤Tµ⌅

� t0

0

dt

a(t)= +⇤

⌃2Dirac�Milne = ⌃2

�CDM

⌅ + 3p < 0

R4

(q, m, a)

D and 3He production by photodisintegration of 4He (ABL & Chardin 12)

Some properties of the Dirac-Milne universe

2nd International Workshop on Antimatter and Gravity University of Bern, November 13 -15, 2013

Albert Einstein Center for Fundamental Physics Sidlerstrasse 5 3012 Bern Switzerland www.einstein.unibe.ch!

Local Organizing Committee: Claude Amsler (Chair) Akitaka Ariga Antonio Ereditato Ciro Pistillo Paola Scampoli James Storey Marcella Esposito (Secretary)

International Advisory Committee: M. Blau (University of Bern, Switzerland) G. Chardin (CNRS/IN2P3, France) M. Doser (CERN, Switzerland) T. Jolicoeur (CNRS/Université Paris-Sud, France) A. Kostelecky (Indiana University, USA) C. Lämmerzahl (University of Bremen, Germany) M. Oberthaler (Heidelberg University, Germany) W. Oelert (Mainz University, Germany) V.V. Nesvizhevsky (ILL, Grenoble, France) P. Perez (CEA, France) Y. Sacquin (CEA, France) G. Testera (INFN Genova, Italy) P. von Ballmoos (IRAP, Toulouse, France) C. Will (University of Florida, USA) Y. Yamazaki (RIKEN, Japan)

http://www.einstein.unibe.ch/WAG2013.html Contact: [email protected]

©!Bern!Tourism!