The quantum Vacuum, Dark Energy & Dark

Matter

Oss. Astron. di Capodimonte 6 September 2012

The Mystery of Concordance Cosmology

The Concordance Cosmology

SN 1999ff(z = 0.455)

SN 1999fv(z 1.21)

The Concordance Cosmology

The Concordance Cosmology

• Described by 2011 Nobel Prize winner Prof. Brian Schmidt as: “A really creepy Universe”

What is Dark Energy?

• This has been the happy hunting ground of theorists. Since January 2012, the following “explanations” have been published:

• Modified Regge calculus model (MORC)• Holographic dark energy• Interacting modified holographic dark energy• Interacting ghost dark energy• Ricci dark energy• Dynamical dark energy• Teleparallel dark energy• Agegraphic dark energy• Interacting polytropic gas dark energy model• High-energy scalaron dark energy

What is Dark Matter?• A similar literature search yields:• Weakly interacting massive particles (WIMPS)• WIMPless dark matter• Higgs-portal dark matter• Bose–Einstein condensate dark matter• Minimal Dark Matter Model• GeV Scale Asymmetric Dark Matter from the Mirror Universe• Higgs decay to dark matter• Sneutrino Dark Matter• Axion Dark Matter• Kaluza-Klein dark matter• Branon dark matter• Light dark matter in leptophobic Z' models• Pseudo-familon dark matter

The Cosmic Coincidence

Mystery

The Cosmic Coincidences• There is a fundamental connection between the parameters of the

Universe and the fundamental constants of nature:

• The Zel’dovich relation connecting the cosmological constant and the mass of a fundamental particle (here undefined):

• The critical acceleration coincidence, connecting a0 (from MOND) with the mass and Compton Wavelength of fundamental particles:

• and the Dirac-Weinberg relation for the Hubble Constant:

Λ ∼ G2m6c2

4

Ho ∼Gmc

2

ao ∼Gm

λ2

Is the Universe a Quantum Black

Hole?

Quantum Black Holes

• Any uncharged, non-rotating Black Hole is characterised by one parameter, its mass.

• Therefore the Schwarzschild Radius:

• and the Compton Wavelength:cannot be independent quantities.

• It follows (He & Ma 2011, Mod.Phys.Lett. A, 26, 2299):

R = 2GM/c2

λ = /Mc

Rλ = 2GL2P ; LP =

G/c3

• If the Universe itself can be regarded as a Black Hole, the entropy is (Fullana & Alfonso-Faus 2012, Ap&SS, 337, 19

• This is the same number as derived from first principles by Egan & Lineweaver 2010 ApJ, 710, 1825)!

• Thus we can interpret the Universe as a QBH with ~10122 bits.

• The quantum mass, mq , derived from the Hawking-Unruth Temperature T is:

• And we find (as we should for a QBH):

The Universe as a Quantum Black Hole (QBH)

S =kBA

4L2p

= π

R

Lp

2

kB ∼ 10122kB

∆E = kBT = R/2πc = mqc2 : mq ∼ 1.7× 10−66 gm

M ∼ 10122mq

The Solution to the Mysteries?

Two big new ideas:

• Villata: CPT-invariance & General Relativity require that anti-matter is real matter traveling in reversed time, and it follows that anti-matter sees anti-gravity with respect to normal matter (but sees normal gravity wrt anti-matter) Villata, M. 2011, EPL (Europhysics Letters), 94, 20011 & Villata, M. Ap&SS 2012 337, 3

• Hajdukovic: The sea of virtual particles in the quantum vacuum is filled with particle-antiparticle pairs which individually act as gravitational dipoles (in an analogous way to electric dipoles) Hajdukovic, D. S. 2010, Ap&SS, 326, 3 Hajdukovic, D. S. 2011, Ap&SS 334, 215 Hajdukovic, D. S. 2012, Ap&SS 337, 9 & Ap&SS in press

• They are probably pions, these being the simplest combinations of up and down quark pairs viz:

• Distance between virtual particle and anti-particle must be less than the reduced Compton wavelength:

• The Gravitational Dipole Moment of the Particle-Antiparticle pair is:

What is the nature of virtual particles in the quantum vacuum?

π+ : ud π− : ud

λπ = /mc

p = mπd |p| < /c

Free Space: Dark Energy

Hypothesis: Dark energy is the energy associated with the virtual gravitational dipoles in the quantum vacuum.

In Presence of a Gravitating Mass: Dark Matter

Hypothesis: A gravitating mass polarizes the virtual gravitational dipoles in the quantum vacuum. Dark matter is the gravitational dipole energy

• Number density of virtual pairs:

• Gravitational Dipole Energy Density:

• giving an effective mass energy density:

Dark Energy

ρE = p.g ×N0

ρM =3g

4πc3λ3π

ρM =3R0

4πc3λ3π

∼ 7.4× 10−30g.cm−3

c.f. ρDE ∼ 7.2× 10−30g.cm−3

N0 ∼ 3/4πλ3π

ρE =3g

4πcλ3π

λπ = /mc

A Different Formulation

• If we substitute for the acceleration (derived below):

• And for the Compton Wavelength:

• We get:

• This is the Zeldovich Sov. Phys. Usp. 24, 216 (1981) formula also derived by Santos Ap&SS 326, 7 (2010) from consideration of the 2-particle correlation function in the quantum vacuum.

λπ = /mc

ρM =√

3Gm6πc2

4π4

R0 = a0 =Gmπ√

3λ2π

Another way to get Dark Energy Density

• The Energy of the Quantum Vacuum (assumed to be gravitational monopoles of mass m! is given by the Quantum Field Theory of Weinberg, 1989:

• ....this is ~ 1040 times too large!

• However, if it is really dipoles, these have a field at large distance ~ ~ 1040 weaker, viz.:λπ/R0

ρE =πmπ

2λ2πR0

∼ 3.1× 10−29 g.cm−3

ρE =πmπ

2λ3π

• The cosmological acceleration is given by:

• Where pressure and energy density are connected through the relativistic equation of state:

• and density transforms as:

• Radiation:

• Matter:

• Classical Dark Energy:

Standard Equation of State

R = −4πGR

3

n

ρn +

3pn

c2

pn = wnρnc2

ρn = ρn0

R0

R

n

w = 1/3 : n = 4

w = 0 : n = 3

w = −1 : n = 0

• We require both the following:

• These imply an effective (component summed) equation of state:

• where Lp is the Planck Length:

• This implies

Equation of State of Gravitational Dipole Dark Energy

pv = −13

1 +

ρm

ρv+

λ3π

L2P R

ρvc

2 ≡ weffρvc2

R = −4πGR

3

n

ρn +

3pn

c2

R0 = ρvc

2 4πcλ3π

3 ;

Lp =

(G/c3)

w0 ∼ −0.99 : w∞ = −1/3

The Dirac-Weinberg Relation

• The mysterious Dirac-Weinberg relation connecting the Hubble Constant with the mass of fundamental particles is:

• In fact, this fails by a factor of ~12, and we need either m! or c varying with time, or H/R to stay constant in order for it to be true at all times

• However, the Dark Energy hypothesis:

• Provides a “complete” Dirac-Weinberg relation of the right magnitude today and without these problems going forward:

ρV =3R

4πc3λ3π

H

3π3

cHΩV

R

=

m3πGc

2

H =m

3πGc

2

• The gravitational dipole moment of particle-antiparticle pair is:

• With all dipoles aligned, the gravitational dipole field is:

• which will occur above a critical field equivalent to the gravitational acceleration of a pion at its own Compton Wavelength:

• With gives

Gravitational Polarization

p = mπd |p| < /c

|−→P g| ≡ Pmax =Aλ3

πc

Pmax =gcr

4πG

∼√

3ao

B ∼ 1√3;A ∼ 1

2√

3

gcr =BGmπ

λ2π

= 2.1× 10−8cm/s−2

Surface Density of “Dark Matter”

• The dark matter density can be interpreted as the density of gravitational polarization charges:

• with maximum polarization gives:

• From which it follows that surface density of dark matter:

ρDM(r) = − .−→P g =

1r2

d

dr(r2Pg(r))

rρDM(r) =√

3λ3mc

ΣDM =mπ

4π√

3λ2π

= 0.0146 g.cm−2 = 70M⊙ pc−2

from Kormendy & Freeman , Dark Matter in Galaxies, IAU Symposium 220, 377 (2004)

Prediction of Theory

Conclusions

• The universe is a Quantum Black Hole with ~10122 bits.

• The quantum vacuum is a sea of virtual pions and anti-pions forming gravitational dipoles.

• Dark energy is nothing more than the dipole energy associated with the pion anti-pion pairs.

• Dark matter is nothing more than the polarization energy associated with the pion anti-pion pairs.

Outcomes

• We derive the entropy of the universe.

• We recover both a modified Dirac-Weinberg relation and also derive the Zeldovich relation.

• We predict the current dark energy density.

• We predict a very different future for the expansion of the Universe (w = -1/3 not -1).

• We obtain the MOND critical acceleration, a0.

• We obtain the observed dark matter surface density of galaxies.

Conclusion

“People are needed who believe in impossible things, in order to make them become real”

Terry Pratchett