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Galileons & Massive Gravity

Galileons & Massive Gravity. Claudia de Rham Dec. 18 th 2013. Why Modify Gravity in the IR ?. Late time acceleration & CC problem. First signs of the breakdown of GR on cosmological scales ?. MG from Extra Dimensions.

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Galileons & Massive Gravity

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  1. Galileons & Massive Gravity Claudia de Rham Dec. 18th 2013

  2. Why Modify Gravity in the IR ? Late time acceleration & CC problem First signs of the breakdown of GRon cosmological scales ?

  3. MG from Extra Dimensions • Best way to obtain a sensible theory of Modified Gravity is to start with General Relativity 5d Gravity Soft massive Gravity (DGP) Hard massive Gravity Ghost-free mGR Galileons

  4. 5d Gravity 4d gravity Infinite extra dimensionConfine Gravity on a brane DGP model DvaliGabadadzePorrati, 2000

  5. 5d Gravity 5d Gravity 4d gravity Infinite extra dimensionConfine Gravity on a brane DGP model Finite-size extra dimensionKK or deconstruction Hard massive Gravity(or multi-gravity)

  6. MG from Extra Dimensions ensures In both cases (DGP and hard mass gravity), 5 dof from massless spin-2 in 5d 5 dof for massive spin-2 in 4d (no BD ghost)

  7. MG from Extra Dimensions ensures In both cases (DGP and hard mass gravity), 5 dof from massless spin-2 in 5d 5 dof for massive spin-2 in 4d (no BD ghost) In both cases, the scalar dof behaves as a Galileon scalar field (in some limit) Screened via Vainshtein mechanism

  8. Deconstructing Gravity 5d Gravity y Deconstruction: Arkani-Hamed, Cohen & Georgi, PRL 86, 4757 (2001) Start with 5d gravity Discretize it along the extra dimension (after gauge fixing)

  9. Deconstructing Gravity 5d Gravity y Start with 5d gravity Discretize it along the extra dimension (after gauge fixing)

  10. Deconstructing Gravity 5d Gravity y Start with 5d gravity Discretize it along the extra dimension (after gauge fixing)

  11. Ghost-free Massive Gravity • Deconstructing 5d GR naturally leads to a 4d Ghost-free multi-gravity theory

  12. Ghost-free Massive Gravity • Deconstructing 5d GR naturally leads to a 4d Ghost-free multi-gravity theory CdR, Matas & Tolley, 1308.4136

  13. Ghost-free Massive Gravity • Deconstructing 5d GR in a gauge-fixed way (5d lapse=1)leads to Ghost-free massive gravity or multi-gravity • Truncated theory is consistent • Deconstruction is EQUIVALENT to KK (after non-linear field redefinition) mass CdR, Matas & Tolley, 1308.4136

  14. Ghost-free Massive Gravity • Structure of mass term is essential to avoid BD ghost Boulware& Deser, PRD 6, 3368 (1972) CdR & Gabadadze, PRD 82, 044020 (2010) CdR, Gabadadze & Tolley, PRL 106, 231101 (2011)

  15. Ghost-free Massive Gravity • Structure of mass term is essential to avoid BD ghost • Helicity-0 mode appears as a Galileon (in some limit) After Stückelbergisation Boulware& Deser, PRD 6, 3368 (1972) CdR & Gabadadze, PRD 82, 044020 (2010) CdR, Gabadadze & Tolley, PRL 106, 231101 (2011)

  16. Ghost-free Massive Gravity • Structure of mass term is essential to avoid BD ghost • Helicity-0 mode appears as a Galileon (in some limit) After Stückelbergisation Boulware& Deser, PRD 6, 3368 (1972) CdR & Gabadadze, PRD 82, 044020 (2010) CdR, Gabadadze & Tolley, PRL 106, 231101 (2011)

  17. Open Questions in MG • Viable Cosmological Solutions & Phenomenology • Quantum Corrections - is the small mass technically natural ? - how does the special structure of the potential gets affected by QC ? • Superluminalities • Strong Coupling

  18. Tuning of the Mass • We typically consider the graviton mass to besame tuning as for the CC problem !

  19. Tuning of the Mass • We typically consider the graviton mass to besame tuning as for the CC problem ! • However the graviton mass is stable against quantum corrections Technically natural tuning, unlike the tuning of the CC to zero

  20. Non-renormalization • In the DL, we recover a Galileon theory which enjoys a non-renormalization theoremgraviton mass does not get renormalized in the DL • Beyond the DL, the graviton mass gets renormalized by CdR, Gabadadze, Heisenberg & Pirtskhalava, 1212.4128 Technically natural tuning, unlike the tuning of the CC to zero

  21. Open Questions in MG • Viable Cosmological Solutions & Phenomenology • Quantum Corrections - is the small mass technically natural ? - how does the special structure of the potential gets affected by QC ? • Superluminalities • Strong Coupling See CdR, Heisenberg & Ribeiro, 1307.7169

  22. Galileons in trouble (?) Perturbations about a background

  23. Galileons in trouble (?) • Change the kinetic structure !!! • Fluctuations see a different effective metric • Fluctuations can propagate faster than light ! Adams, Arkani-Hamed, Dubovsky, Nicolis & Rattazzi, JHEP 0610 (2006) 014 Hinterbichler, Nicolis & Porrati, JHEP 0909, 089 (2009) Burrage, CdR, Heisenberg & Tolley, JCAP 1207, 004 (2012)Deser & Waldron, PRL 110, 111101 (2013)

  24. Galileons in trouble (?) • Strong coupling scale gets redressed: At the surface of the Earth(only from the effect of the Earth)

  25. Galileons in trouble (?) • Strong coupling scale gets redressed: • After that ? … break tree-level unitarity At the surface of the Earth(only from the effect of the Earth)

  26. Galileons in trouble (?) Strong Coupling Issues & SuperluminalitiesUbiquitous to Galileon theories& to massive gravity (?) This was the state of Affairs …till the end of 2012

  27. 2012 Breakthrough • July: Higgs Boson discovered • August: Curiosity Lands on Mars • Summer: Quantum Teleportation Distance Record Broken of more than 50 miles • October: Earth’s ExoplanetTwin discovered orbiting Alpha Centauri B • December 31st 2012 @ 20:55:59 GMT: …

  28. 2012 Breakthrough • July: Higgs Boson discovered • August: Curiosity Lands on Mars • Summer: Quantum Teleportation Distance Record Broken of more than 50 miles • October: Earth’s ExoplanetTwin discovered orbiting Alpha Centauri B • December 31st 2012 @ 20:55:59 GMT:

  29. Missed the final breakthrough because… December 31st2012, 20:55:59 GMT

  30. Dual Galileon In 3d

  31. Dual Galileon In 3d Curtright& Fairlie, 1212.6972 CdR, Fasiello & Tolley, 1308.2702 + in preparation

  32. Dual Galileon In 3d Curtright& Fairlie, 1212.6972 CdR, Fasiello & Tolley, 1308.2702 + in preparation

  33. Dual Galileon Large x no Vainshtein Small x Vainshtein Large Large Small Vainshtein region inoriginal theory mapsto weak region in dual theory.

  34. Dual Galileon Canonical normalization of r:

  35. Dual Galileon Canonical normalization of r: Strong coupling Weak coupling

  36. Strong Coupling in the Dual theory • The dual theory is under control as long as • Back to the original theory, this implies For the Earth CdR, Fasiello & Tolley, 1308.2702 + in preparation

  37. Other eg. of duality In 4d

  38. Other eg. of duality In 4d

  39. Other eg. of duality • The original theory admits superluminal propagationin the vacuum ! (ie. no matter or other sources)

  40. Other eg. of duality • The original theory admits superluminal propagationin the vacuum ! (ie. no matter or other sources)plane wave solutions

  41. Other eg. of duality • The original theory admits superluminal propagationin the vacuum ! (ie. no matter or other sources)plane wave solutions • Speed of fluctuations: Superluminal propagation for

  42. Other eg. of duality • The original theory admits superluminal propagation • Yet the dual theory is just free ! • Trivially causal, unitary, UV complete,…

  43. Group vs Front velocity • In the original theory,What is SL is the GROUP velocity • What counts for causality is the FRONT velocity here

  44. Group vs Front velocity • In the original theory,What is SL is the GROUP velocity • What counts for causality is the FRONT velocity • Duality implies that the front velocity is LUMINAL No acausality

  45. Outlook • Massive Gravity is a specific framework to study IR modifications of Gravity • It could play a role for - the late-time acceleration of the Universe - the cosmological constant problem • We now have the theoretical formalism to describe a stable theory of massive gravity • It behaves a scalar-tensor Galileon theory in some limit, hand in hand with a Vainshtein mechanism

  46. Outlook • Galileon theories are plagued with bothSuperluminalities & Strong Issues • These issues could be tackled by a field redefinition DUAL GALILEON ? • Massive Gravity requires tuningThe graviton mass is technically naturalAt 1-loop the potential does not get strongly distabilizedAt higher loops, it still need to be explored…

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