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Learning with Pierre: from branes to gravity
Cédric Deffayet (IAP and IHÉS, CNRS Paris)
Les Houches 1999 « the primordial Universe »
APC, May the 3rd 2018
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(Sur certains aspects géométriques des théories conformes bidimensionnelles)
(Mécanismes de brisure de supersymétrie)
(Étude de la brisure de symétries dans des théories de cordes et de supergravité)
(Le problème des hiérachies de masse dans les modèles supersymétriques)
(Aspects cosmologiques des théories de supercordes)
- Jean-François Dufaux 2004
(Modèles branaires en théories de gravité généralisées)
(Search for beyond the standard model physics at the CMS experiment : supersymmetry and extra dimensions)
(Production d'ondes gravitationnelles par les cordes cosmiques avec jonctions)
(Beyond the trapping horizon : the apparent universe & the regular black hole)
(Classification des modèles d’inflation et contraintes sur la physique fondamentale)
The PhD students of Pierre
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(Sur certains aspects géométriques des théories conformes bidimensionnelles)
(Mécanismes de brisure de supersymétrie)
(Étude de la brisure de symétries dans des théories de cordes et de supergravité)
(Le problème des hiérachies de masse dans les modèles supersymétriques)
(Aspects cosmologiques des théories de supercordes)
- Jean-François Dufaux 2004
(Modèles branaires en théories de gravité généralisées)
(Search for beyond the standard model physics at the CMS experiment : supersymmetry and extra dimensions)
(Production d'ondes gravitationnelles par les cordes cosmiques avec jonctions)
(Beyond the trapping horizon : the apparent universe & the regular black hole)
(Classification des modèles d’inflation et contraintes sur la physique fondamentale)
The PhD students of Pierre
Cosmology Gravitation High energy theoretical physics
SLIDE 4 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)
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Then my PhD director at Orsay LPT on « Cosmological aspects of superstring theories »
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« 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
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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
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Very good timing for the interests of Pierre !
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I started my PhD in sept 1997…. … after one year….
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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)
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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 !
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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)
Brane cosmology Brane gravity
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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
SLIDE 14 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
SLIDE 15 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
Contains brane localized sources Newton constant GNewton
SLIDE 16 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
Newton constant GNewton
Einstein equations
Not suitable for cosmology ! Contains brane localized sources
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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 !
SLIDE 18 Geometrical relations between
(5)
- Intrinsic curvature (4D) : G
(4)
- Extrinsic curvature: K
5D Curvature Intrinsic curvature Quadratic in the extrinsic curvature
Generalized Gauss identities:
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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 + …
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I.e. we get Or in cosmology
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This applies generically to brane worlds (of codimension 1) E.g. 1.: Randall-Sundrum model (bulk is AdS5)
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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 :
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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
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(C.D. 2000)
SLIDE 25 First concrete proposal to link the acceleration of the expansion
- f 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
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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)
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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
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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)
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)
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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)
SLIDE 30 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)
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Back to 1999
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GPS (of the GDR): « Groupe de Priorité Supersymétrique » …
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Not to be confused with the « Groupe de Pelotons de Sécurité » (20 april 1999: « affaire des Paillottes » in Corsica …)
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Not to be confused with the « Groupe de Pelotons de Sécurité » (20 april 1999: « affaire des Paillottes » in Corsica …) Cargèse, Corsica summer 1998
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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….
