Learning with Pierre: from branes to gravity Cédric Deffayet (IAP and IHÉS, CNRS Paris) APC, May the 3rd 2018 Les Houches 1999 « the primordial Universe »
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 • 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) High energy Stéphane Lavignac 1997 • theoretical physics (Le problème des hiérachies de masse dans les modèles supersymétriques) C.D. 2000 • (Aspects cosmologiques des théories de supercordes) Cosmology 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) Gravitation 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)
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 »
1994- Scientific context: « Second string revolution » High energy theory and discovery of the string web of dualities ADS-CFT correspondance (Maldacena) 1997- Role played there by « D(irichlet)-branes » Brane-localized degrees of freedom
Scientific context: Cosmology 1998- Discovery of the acceleration of the expansion of the Universe (SCP and HZT teams 1998, Nobel prize 2011) Launch of WMAP mission (june 2001) 2001- Advent of « Precision 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)
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 !
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 gravity Brane cosmology
1998- Arkani-Hamed, Dimopoulos, Dvali (ADD) brane worlds « brane-worlds » 1999- Randall-Sundrum (RS) models 2000- Dvali-Gabadadze-Porrati (DGP) models Usual space-time (4 dimensions): gravity that of a brane Bulk space-time has 4+n dimensions
In ADD or RS brane worlds, the gravity potential V(r) between brane localized sources behaves as in 3+1 dimensions at large distances This result is obtained by perturbation theory (with a localized source) Newton constant G Newton I.e. one solves for h ¹ º defined by Metric on the brane g ¹ º = g (0) ¹ º + h ¹ º Small perturbation « generated » by a Background localized matter metric source Einstein equations
In ADD or RS brane worlds, the gravity potential V(r) between brane localized sources behaves as in 3+1 dimensions at large distances This result is obtained by perturbation theory (with a localized source) Newton constant G Newton I.e. one solves for h ¹ º defined by Metric on the brane g ¹ º = g (0) ¹ º + h ¹ º Contains brane localized sources Small perturbation « generated » by a Background localized matter metric source Einstein equations
In ADD or RS brane worlds, the gravity potential V(r) between brane localized sources behaves as in 3+1 dimensions at large distances This result is obtained by perturbation theory (with a localized source) Newton constant G Newton I.e. one solves for h ¹ º defined by Not suitable for cosmology ! Metric on the brane g ¹ º = g (0) ¹ º + h ¹ º Contains brane localized sources Small perturbation « generated » by a Background localized matter metric source Einstein equations
Some space geometry ! 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.
Geometrical relations between • 5D curvature: G AB (5) • Intrinsic curvature (4D) : G (4) • Extrinsic curvature: K Generalized Gauss identities: Intrinsic Quadratic in the curvature 5D Curvature extrinsic curvature
Using this decomposition into Einstein equations (with a distributional source) 1/ By equating the distributional source, we get: Extrinsic Energy-momentum Curvature tensor » 2/ Inserting this is the generalized Gauss identities we find Kown by the buk » H 2 + … Quadratic in S ¹ º ( or ) Einstein equations
I.e. we get Or in cosmology
This applies generically to brane worlds (of codimension 1) E.g. 1.: Randall-Sundrum model (bulk is AdS 5 )
E.g. 2.: Dvali-Gabadadze-Porrati (DGP 2000) model (bulk is Minkowski 5 ) Pertubation theory : The Newton potential (computed perturbatively) behaves as However this is mediated by a resonance of massive gravitons and hence
E.g. 2.: Dvali-Gabadadze-Porrati (DGP 2000) model (bulk is Minkowski 5 ) Cosmology (applying the technique of our 1999 paper) : Equating the distributional source in the 5D Einstein equation still yields But now Inserting this is the generalized Gauss identities 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) 2016 « Modified gravity » and « cosmology » (from WoS) 2000 2016 « Modified gravity » (from WoS) 2000
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)
This quadratic structure comes from the generalized Gauss identities 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 » ( Together with ) yielding a scalar theory with second order quadratic equations of motions (Luty, Porrati, Rattazzi, 2003)
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) 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)
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