Learning with Pierre: from branes to gravity · Revival of « massive gravity » via the Vainshtein mechanism (First) attempt to give a mass to the graviton: Fierz and Pauli 1939

Learning with Pierre:

from branes to gravity

Dire ici que pas tout est présenté

Cédric Deffayet

(IAP and IHÉS, CNRS Paris)

Les Houches 1999

« the primordial Universe »

APC, May the 3rd 2018

• Frank Thuiller 1991 (Sur certains aspects géométriques des théories conformes bidimensionnelles)

• Emilian Dudas 1994 (Mécanismes de brisure de supersymétrie)

• François Pillon 1995 (Étude de la brisure de symétries dans des théories de cordes et de supergravité)

• Stéphane Lavignac 1997 (Le problème des hiérachies de masse dans les modèles supersymétriques)

• C.D. 2000 (Aspects cosmologiques des théories de supercordes)

• Jean-François Dufaux 2004 (Modèles branaires en théories de gravité généralisées)

• Leonardo Sala 2009 (Search for beyond the standard model physics at the CMS experiment : supersymmetry and extra dimensions)

• Alejandro Bohé 2011 (Production d'ondes gravitationnelles par les cordes cosmiques avec jonctions)

• Alexis Helou 2015 (Beyond the trapping horizon : the apparent universe & the regular black hole)

• Mauro Pieroni 2016 (Classification des modèles d’inflation et contraintes sur la physique fondamentale)

The PhD students of Pierre

• Frank Thuiller 1991 (Sur certains aspects géométriques des théories conformes bidimensionnelles)

• Emilian Dudas 1994 (Mécanismes de brisure de supersymétrie)

• François Pillon 1995 (Étude de la brisure de symétries dans des théories de cordes et de supergravité)

• Stéphane Lavignac 1997 (Le problème des hiérachies de masse dans les modèles supersymétriques)

• C.D. 2000 (Aspects cosmologiques des théories de supercordes)

• Jean-François Dufaux 2004 (Modèles branaires en théories de gravité généralisées)

• Leonardo Sala 2009 (Search for beyond the standard model physics at the CMS experiment : supersymmetry and extra dimensions)

• Alejandro Bohé 2011 (Production d'ondes gravitationnelles par les cordes cosmiques avec jonctions)

• Alexis Helou 2015 (Beyond the trapping horizon : the apparent universe & the regular black hole)

• Mauro Pieroni 2016 (Classification des modèles d’inflation et contraintes sur la physique fondamentale)

The PhD students of Pierre

Cosmology

Gravitation

High energy

theoretical physics

Cosmology

Gravitation

High energy

theoretical physics

Pierre was first my professor at the ENS (in 1993) where he was teaching

(special) relativity and then at the « master 2 » « CPM »

Promotion 1996 (thanks to F. Derue)

Then my PhD director at Orsay LPT on

« Cosmological aspects of superstring theories »

« Second string revolution »

and discovery of the string web of dualities

Brane-localized

degrees of freedom

Role played there by

« D(irichlet)-branes »

ADS-CFT correspondance (Maldacena)

1994-

1997-

Scientific context:

High energy theory

1998- Discovery of the acceleration of the expansion of the Universe

(SCP and HZT teams 1998, Nobel prize 2011)

2001- Launch of WMAP mission (june 2001)

Advent of « Precision cosmology »

Scientific context:

Cosmology

Very good timing for the

interests of Pierre !

I started my PhD

in sept 1997….

… after one year….

Today: I am going to discuss some long lasting fruits of a

simple equation obtained in our paper of 1999 : (the most cited paper of Pierre with more than 1000 citations)



19 years today !



Brane cosmology

Brane gravity

1998- Arkani-Hamed, Dimopoulos, Dvali (ADD) brane worlds

1999- Randall-Sundrum (RS) models

2000- Dvali-Gabadadze-Porrati (DGP) models

« brane-worlds »

Usual space-time

(4 dimensions):

that of a brane gravity

Bulk space-time has

4+n dimensions

This result is obtained by perturbation

theory (with a localized source)

I.e. one solves for h¹ º defined by

g¹ º = g(0)¹ º + h¹ º

Background

metric

Metric on the brane

Small perturbation

« generated » by a

localized matter

source

In ADD or RS brane worlds, the gravity potential V(r) between brane

localized sources behaves as in 3+1 dimensions at large distances

Einstein equations

Newton constant GNewton




g¹ º = g(0)¹ º + h¹ º

Background

metric

Metric on the brane

Small perturbation


localized matter

source



Einstein equations

Contains brane localized sources





g¹ º = g(0)¹ º + h¹ º

Background

metric

Metric on the brane

Small perturbation


localized matter

source




Einstein equations

Not suitable for cosmology !

Contains brane localized sources

The brane localized matter is only sensitive

to the “curvature” of the metric on the

brane (and not the one of the bulk) …

… i.e. to the “intrinsic curvature” of the

surface mesured e.g. by G (4) .

The embedding of the surface into the

defines a so called “extrinsic curvature”

measured by a tensor K

Ex: vs.

Some space geometry !

Geometrical relations between

•5D curvature: GAB(5)

•Intrinsic curvature (4D) : G (4)

•Extrinsic curvature: K

5D Curvature

Intrinsic

curvature Quadratic in the

extrinsic curvature

Generalized Gauss identities:

1/ By equating the distributional source, we get:

Using this decomposition into Einstein equations (with

a distributional source)

Extrinsic

Curvature Energy-momentum

tensor »

2/ Inserting this is the generalized Gauss identities we find

Kown by the buk

Einstein equations Quadratic in S¹ º ( or ) » H2 + …

I.e. we get

Or in cosmology

This applies generically to brane worlds (of codimension 1)

E.g. 1.: Randall-Sundrum model (bulk is AdS5)

E.g. 2.: Dvali-Gabadadze-Porrati (DGP 2000) model (bulk is Minkowski5)

The Newton potential (computed perturbatively) behaves as

However this is mediated by a resonance of massive gravitons

and hence

Pertubation theory :

E.g. 2.: Dvali-Gabadadze-Porrati (DGP 2000) model (bulk is Minkowski5)

Cosmology (applying the technique of our 1999 paper) :

Equating the distributional source in the 5D Einstein equation

still yields

Inserting this is the generalized Gauss identities

But now

We get now a quadratic equation for the Hubble factor H

(C.D. 2000)

First concrete proposal to link the acceleration of the expansion

of the Universe to a large distance modification of gravity

(CD 2000; CD, Dvali, Gabadadze 2001)

« Modified gravity » and « cosmology » (from WoS)

« Modified gravity » (from WoS)

2000

2000

2016

2016

Lead to a new phenomenology of scalar-tensor theories via the

« Galileons » and friends.

The DGP model has a strong coupling in the scalar

sector (CD, Dvali, Gabadadze, Vainshtein, 2002)

This can be extracted taking a « decoupling limit »

yielding a scalar theory with second order quadratic

equations of motions

(Luty, Porrati, Rattazzi, 2003)









(

(Together with )

This quadratic structure comes from the generalized Gauss identities

Generalized to Galileons (Nicolis, Rattazzi, Trincherini, 2009),

covariant Galileons (CD, Esposito-Farese, Vikman, 2009) ,

and the more recent « Beyond Horndeski » theories (Zumalacarregui, Garcia-Bellido, 2014; Gleyzes, Langlois, Piazza,

Vernizzi, 2015)









Revival of « massive gravity » via the Vainshtein mechanism

(First) attempt to give a mass to the graviton:

Fierz and Pauli 1939

A massive and a massless graviton yield drastically

different physical results (e.g. for light bending) (van Dam, Veltman; Zakharov; Iwasaki, 1970)

A way out was suggested by Vainshtein in 1972

Criticized and new obstructions found by Boulware and

Deser in 1972

The DGP cosmology provided the first hint in favour of the

Vainshtein mechanism (CD,Dvali, Gabadadze, Vainshtein 2001)

This lead to new efforts in the search of a consistent theory of

massive gravity using in particular the equivalent of the

decoupling limit of DGP model (Creminelli, Nicolis, Papucci, Trincherini, 2005; CD, Rombouts, 2005)

First explicit proof that the Vainshtein mechanism is working as

expected in massive gravity (Babichev, CD, Ziour, 2009)

Discovery of a family of massive gravity theory devoid of the

Boulware Deser pathologies (de Rham, Gabadadze 2010; de Rham, Gabadadze, Tolley, 2011)

2000

2016

« Massive gravity » (from WoS)

Back to 1999

GPS (of the GDR): « Groupe de Priorité Supersymétrique » …

Not to be confused with the « Groupe de Pelotons de Sécurité »

(20 april 1999: « affaire des Paillottes » in Corsica …)

Not to be confused with the « Groupe de Pelotons de Sécurité »

(20 april 1999: « affaire des Paillottes » in Corsica …)

Cargèse, Corsica

summer 1998

Working under the supervision of

Pierre was very inspiring !

On the physics side,

he was always optimistic !

And also very pleasant on the human side!

We miss him a lot….

Documents

Learning with Pierre: from branes to gravity · Revival of « massive gravity » via the Vainshtein mechanism (First) attempt to give a mass to the graviton: Fierz and Pauli 1939