C. Germani - Sub-Planckian Higgs and Axionic Inflations

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The SEENET-MTP Workshop BW2011
Particle Physics from TeV to Plank Scale
28 August – 1 September 2011, Donji Milanovac, Serbia

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C. Germani - Sub-Planckian Higgs and Axionic Inflations

  1. 1. Introduction Slow roll The failure of Higgs bosonSub-Planckian Higgs and Axionic Inflations New Higgs Inflation Gravitationally Enhanced Friction Cristiano Germani Introducing the Slotheon Based on different collaborations: Martucci, Moyassari, Kehagias, Watanabe Uniqueness Unitarity LMU, ASC, Munich, Germany UV Protected Inflation BW2011, August 2011, Donji Milanovac, Serbia
  2. 2. Introduction Introduction Slow rollLatest cosmological data agree impressively well with the a The failure of Higgs boson Universe which is at large scales New Higgs Inflation Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  3. 3. Introduction Introduction Slow rollLatest cosmological data agree impressively well with the a The failure of Higgs boson Universe which is at large scales New Higgs Inflation Gravitationally Enhanced Friction Introducing the Slotheon homogeneous, Uniqueness Unitarity UV Protected Inflation
  4. 4. Introduction Introduction Slow rollLatest cosmological data agree impressively well with the a The failure of Higgs boson Universe which is at large scales New Higgs Inflation Gravitationally Enhanced Friction Introducing the Slotheon homogeneous, Uniqueness isotropic Unitarity UV Protected Inflation
  5. 5. Introduction Introduction Slow rollLatest cosmological data agree impressively well with the a The failure of Higgs boson Universe which is at large scales New Higgs Inflation Gravitationally Enhanced Friction Introducing the Slotheon homogeneous, Uniqueness isotropic Unitarity spatially flat UV Protected Inflation
  6. 6. Introduction Introduction Slow rollLatest cosmological data agree impressively well with the a The failure of Higgs boson Universe which is at large scales New Higgs Inflation Gravitationally Enhanced Friction Introducing the Slotheon homogeneous, Uniqueness isotropic Unitarity spatially flat UV Protected Inflation A flat FRW Spacetime!
  7. 7. A theoretical puzzle: Introduction Slow roll The failure of Higgs boson A flat FRW Universe New Higgs Inflation ds 2 = −dt 2 + a(t)2 dx · dx Gravitationally Enhanced Friction Introducing theis extremely fine tuned solution of GR! Slotheon Uniqueness Unitarity UV Protected Inflation
  8. 8. A theoretical puzzle: Introduction Slow roll The failure of Higgs boson A flat FRW Universe New Higgs Inflation ds 2 = −dt 2 + a(t)2 dx · dx Gravitationally Enhanced Friction Introducing the is extremely fine tuned solution of GR! Slotheon Uniqueness Unitarity UV Protected Inflation A simple idea to solve this puzzle is Inflation:An exponential (accelerated and homogeneous) expansion of the Early Universe
  9. 9. Introduction Slow roll The failure ofBy geometrical identities (Raychaudhuri equation) Higgs boson New Higgs Inflation Gravitationally ¨ ∝ −( a ρ +3 p ) Enhanced Friction effective energy density effective pressure Introducing the Slotheon ⇓ Uniqueness Unitarity ρ + 3p < 0 , during inflation UV Protected Inflation ρ + 3p > 0 , after inflation
  10. 10. Slow Roll IntroductionA scalar field φ is a good candidate as Slow roll The failure of Higgs boson New Higgs Inflation Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  11. 11. Slow Roll IntroductionA scalar field φ is a good candidate as Slow roll The failure of Higgs boson 1˙ 1˙ ρ = φ2 +V , p = φ2 −V New Higgs 2 2 Inflation Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  12. 12. Slow Roll IntroductionA scalar field φ is a good candidate as Slow roll The failure of Higgs boson 1˙ 1˙ ρ = φ2 +V , p = φ2 −V New Higgs 2 2 Inflation Gravitationally ⇓ Enhanced Friction Introducing the ˙ ρ + 3p ∝ φ2 −V Slotheon Uniqueness Unitarity UV Protected Inflation
  13. 13. Slow Roll Introduction A scalar field φ is a good candidate as Slow roll The failure of Higgs boson 1˙ 1˙ ρ = φ2 +V , p = φ2 −V New Higgs 2 2 Inflation Gravitationally ⇓ Enhanced Friction Introducing the ˙ ρ + 3p ∝ φ2 −V Slotheon Uniqueness Unitarity ⇓ UV Protected Inflation˙2φ V , Inflation happens (“slow roll”)˙φ2 ∼ V , Inflation ends
  14. 14. Slow Roll Introduction A scalar field φ is a good candidate as Slow roll The failure of Higgs boson 1˙ 1˙ ρ = φ2 +V , p = φ2 −V New Higgs 2 2 Inflation Gravitationally ⇓ Enhanced Friction Introducing the ˙ ρ + 3p ∝ φ2 −V Slotheon Uniqueness Unitarity ⇓ UV Protected Inflation˙2φ V , Inflation happens (“slow roll”)˙φ2 ∼ V , Inflation ends Q: Do we know any scalar field?
  15. 15. Slow Roll Introduction A scalar field φ is a good candidate as Slow roll The failure of Higgs boson 1˙ 1˙ ρ = φ2 +V , p = φ2 −V New Higgs 2 2 Inflation Gravitationally ⇓ Enhanced Friction Introducing the ˙ ρ + 3p ∝ φ2 −V Slotheon Uniqueness Unitarity ⇓ UV Protected Inflation˙2φ V , Inflation happens (“slow roll”)˙φ2 ∼ V , Inflation ends Q: Do we know any scalar field? Higgs Boson!!!!
  16. 16. The failure of Higgs boson in GR Introduction Slow roll The Higgs Lagrangian is The failure of Higgs boson 2 √ Mp R 2 New HiggsS= d 4 x −g − Dµ H † D µ H − λ H † H − v 2 Inflation 2 Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  17. 17. The failure of Higgs boson in GR Introduction Slow roll The Higgs Lagrangian is The failure of Higgs boson 2 √ Mp R 2 New HiggsS= d 4 x −g − Dµ H † D µ H − λ H † H − v 2 Inflation 2 Gravitationally Enhanced Friction Introducing the Slotheon All fields but H are subdominant during Inflation Uniqueness Unitarity UV Protected Inflation
  18. 18. The failure of Higgs boson in GR Introduction Slow roll The Higgs Lagrangian is The failure of Higgs boson 2 √ Mp R 2 New HiggsS= d 4 x −g − Dµ H † D µ H − λ H † H − v 2 Inflation 2 Gravitationally Enhanced Friction Introducing the Slotheon All fields but H are subdominant during Inflation Uniqueness Unitary gauge HT = (0, v√2 ) +Φ Unitarity UV Protected Inflation
  19. 19. The failure of Higgs boson in GR Introduction Slow roll The Higgs Lagrangian is The failure of Higgs boson 2 √ Mp R 2 New HiggsS= d 4 x −g − Dµ H † D µ H − λ H † H − v 2 Inflation 2 Gravitationally Enhanced Friction Introducing the Slotheon All fields but H are subdominant during Inflation Uniqueness Unitary gauge HT = (0, v√2 ) +Φ Unitarity UV Protected In order to slow roll Φ v Inflation
  20. 20. The failure of Higgs boson in GR Introduction Slow roll The Higgs Lagrangian is The failure of Higgs boson 2 √ Mp R 2 New HiggsS= d 4 x −g − Dµ H † D µ H − λ H † H − v 2 Inflation 2 Gravitationally Enhanced Friction Introducing the Slotheon All fields but H are subdominant during Inflation Uniqueness Unitary gauge HT = (0, v√2 ) +Φ Unitarity UV Protected In order to slow roll Φ v Inflation ⇓ √ R 1 λ S= d 4 x −g − ∂µ Φ∂ µ Φ − Φ4 2κ2 2 4
  21. 21. Inflation: IntroductionH = a/a ˙ const (exponential expansion) Slow roll ¨ Φ ˙ 3H Φ (slow roll) The failure of Higgs boson New Higgs Inflation Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  22. 22. Inflation: IntroductionH = a/a ˙ const (exponential expansion) Slow roll ¨ Φ ˙ 3H Φ (slow roll) The failure of Higgs boson ⇓ New Higgs Inflation H ˙ Gravitationally ≡ − H2 1 Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  23. 23. Inflation: IntroductionH = a/a ˙ const (exponential expansion) Slow roll ¨ Φ ˙ 3H Φ (slow roll) The failure of Higgs boson ⇓ New Higgs Inflation H ˙ Gravitationally ≡ − H2 1 Enhanced Friction Introducing the Slotheon ⇓ Uniqueness Unitarity Φ Mp !!!! UV Protected Inflation
  24. 24. Inflation: Introduction H = a/a ˙ const (exponential expansion) Slow roll ¨ Φ ˙ 3H Φ (slow roll) The failure of Higgs boson ⇓ New Higgs Inflation H ˙ Gravitationally ≡ − H2 1 Enhanced Friction Introducing the Slotheon ⇓ Uniqueness Unitarity Φ Mp !!!! UV Protected Inflation ⇓R Mp for the Standard Model values of λ ∼ 10−1 ! 2Inflation happens during the Quantum Gravity regime!
  25. 25. Lowering the curvature during Inflation Introduction Recapitulate: Slow roll The failure of Higgs boson New Higgs Inflation Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  26. 26. Lowering the curvature during Inflation Introduction Recapitulate: Slow roll The failure of Higgs boson V (Φ) Φ4 R ∼ H2 ∝ 2 ∝ 2 New Higgs Inflation Mp Mp Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  27. 27. Lowering the curvature during Inflation Introduction Recapitulate: Slow roll The failure of Higgs boson V (Φ) Φ4 R ∼ H2 ∝ 2 ∝ 2 New Higgs Inflation Mp Mp Gravitationally Enhanced Friction ˙ Φ −Mp Φ Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  28. 28. Lowering the curvature during Inflation Introduction Recapitulate: Slow roll The failure of Higgs boson V (Φ) Φ4 R ∼ H2 ∝ 2 ∝ 2 New Higgs Inflation Mp Mp Gravitationally Enhanced Friction ˙ Φ −Mp Φ Introducing the Slotheon Uniqueness ˙ ˙ 2 H Φ2 Mp Unitarity =− 2 ∝ 2 2 ∼ 2 1⇒Φ Mp H H Mp Φ UV Protected Inflation ⇓ R 2 Mp
  29. 29. Lowering the curvature during Inflation Introduction Recapitulate: Slow roll The failure of Higgs boson V (Φ) Φ4 R ∼ H2 ∝ 2 ∝ 2 New Higgs Inflation Mp Mp Gravitationally Enhanced Friction ˙ Φ −Mp Φ Introducing the Slotheon Uniqueness ˙ ˙ 2 H Φ2 Mp Unitarity =− 2 ∝ 2 2 ∼ 2 1⇒Φ Mp H H Mp Φ UV Protected Inflation ⇓ R 2 Mp Solution: Increase the friction!
  30. 30. Introduction New Higgs Inflation Slow roll The failure of Higgs bosonHow to increase the friction: New Higgs Inflation Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  31. 31. Introduction New Higgs Inflation Slow roll The failure of Higgs bosonHow to increase the friction: New Higgs Inflation ˙ ˙ 2if Φ → Ω Φ with Ω 1 Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  32. 32. Introduction New Higgs Inflation Slow roll The failure of Higgs bosonHow to increase the friction: New Higgs Inflation ˙ ˙ 2if Φ → Ω Φ with Ω 1 Gravitationally Enhanced Friction then Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  33. 33. Introduction New Higgs Inflation Slow roll The failure of Higgs boson How to increase the friction: New Higgs Inflation ˙ ˙2 if Φ → Ω Φ with Ω 1 Gravitationally Enhanced Friction then Introducing the Slotheon ˙ 2 2 Φ2 Mp 2 Mp Uniqueness∝ ∼ 2 4 1 → Mp R (for large enough Ω) Unitarity H 2 Mp 2 Φ Ω Ω8 UV Protected Inflation
  34. 34. Introduction New Higgs Inflation Slow roll The failure of Higgs boson How to increase the friction: New Higgs Inflation ˙ ˙ 2 if Φ → Ω Φ with Ω 1 Gravitationally Enhanced Friction then Introducing the Slotheon ˙ 2 2 Φ2 Mp 2 Mp Uniqueness∝ ∼ 2 4 1 → Mp R (for large enough Ω) Unitarity H 2 Mp 2 Φ Ω Ω8 UV Protected Inflation Quantum Gravity regime is avoided during Inflation!
  35. 35. IntroductionGravitationally Enhanced Friction (GEF) Slow roll The failure of Higgs boson The friction should only be efficient at high energies: New Higgs df Ω2 ∼ 3µH = f (H), dH ≥0 Inflation Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  36. 36. IntroductionGravitationally Enhanced Friction (GEF) Slow roll The failure of Higgs boson The friction should only be efficient at high energies: New Higgs df Ω2 ∼ 3µH = f (H), dH ≥0 Inflation Gravitationally Enhanced Friction A typical (positive) enhancement could be Introducing the H2 µ=1+ M2 Slotheon Uniqueness Unitarity UV Protected Inflation
  37. 37. IntroductionGravitationally Enhanced Friction (GEF) Slow roll The failure of Higgs boson The friction should only be efficient at high energies: New Higgs df Ω2 ∼ 3µH = f (H), dH ≥0 Inflation Gravitationally Enhanced Friction A typical (positive) enhancement could be Introducing the H2 µ=1+ M2 Slotheon UniquenessIf no new d.o.f. are added, the scalar e.o.m. can only be Unitarity ¨ ˙ t µ ˙ UV Protected µ Φ + 3H Φ = −V → teff √ µ as µH 1 Inflation
  38. 38. Introduction Gravitationally Enhanced Friction (GEF) Slow roll The failure of Higgs boson The friction should only be efficient at high energies: New Higgs df Ω2 ∼ 3µH = f (H), dH ≥0 Inflation Gravitationally Enhanced Friction A typical (positive) enhancement could be Introducing the H2 µ=1+ M2 Slotheon Uniqueness If no new d.o.f. are added, the scalar e.o.m. can only be Unitarity ¨ ˙ t µ ˙ UV Protected µ Φ + 3H Φ = −V → teff √ µ as µH 1 InflationIf H M the scalar field clock is frozen w.r.t. the observer and friction is enhanced.
  39. 39. IntroductionGravitationally Enhanced Friction: Realization Slow roll The failure of We promote the rescaling to all coords. Higgs boson √ H2 ∂µ → µ∂µ , µ = 1 + M 2 New Higgs Inflation Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  40. 40. IntroductionGravitationally Enhanced Friction: Realization Slow roll The failure of We promote the rescaling to all coords. Higgs boson √ H2 ∂µ → µ∂µ , µ = 1 + M 2 New Higgs Inflation Gravitationally G αβ −H 2 g αβ during Inflation Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  41. 41. IntroductionGravitationally Enhanced Friction: Realization Slow roll The failure of We promote the rescaling to all coords. Higgs boson √ H2 ∂µ → µ∂µ , µ = 1 + M 2 New Higgs Inflation Gravitationally G αβ −H 2 g αβ during Inflation Enhanced Friction Introducing the Slotheon G µν g µν ∂ µ Φ∂ν Φ → g µν − M2 ∂µ Φ∂ν Φ Uniqueness Unitarity UV Protected Inflation
  42. 42. Introduction Gravitationally Enhanced Friction: Realization Slow roll The failure of We promote the rescaling to all coords. Higgs boson √ H2 ∂µ → µ∂µ , µ = 1 + M 2 New Higgs Inflation Gravitationally G αβ −H 2 g αβ during Inflation Enhanced Friction Introducing the Slotheon G µν g µν ∂ µ Φ∂ν Φ → g µν − M2 ∂µ Φ∂ν Φ Uniqueness Unitarity UV Protected New Higgs Inflation Lagrangian Inflation √ R 1 G αβ λ 4S= d 4 x −g 2 − g αβ − ∂α Φ∂β Φ − Φ 2κ 2 M2 4
  43. 43. IntroductionThe New Higgs inflation is a Slotheonic theory Slow roll 1 G αβ The failure of LK = − g αβ − ∂α Φ∂β Φ Higgs boson 2 M2 New Higgs Inflation Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  44. 44. Introduction The New Higgs inflation is a Slotheonic theory Slow roll 1 G αβ The failure of LK = − g αβ − ∂α Φ∂β Φ Higgs boson 2 M2 New Higgs InflationThe name comes to the fact that on a given metric Gravitationally Enhanced Friction ˙ G tt ˙ Introducing the HK ∼ Φ 2 1 + 2 ≥ Φ2 Slotheon M Uniqueness Unitarity UV Protected Inflation
  45. 45. Introduction The New Higgs inflation is a Slotheonic theory Slow roll 1 G αβ The failure of LK = − g αβ − ∂α Φ∂β Φ Higgs boson 2 M2 New Higgs Inflation The name comes to the fact that on a given metric Gravitationally Enhanced Friction ˙ G tt ˙ Introducing the HK ∼ Φ 2 1 + 2 ≥ Φ2 Slotheon M Uniqueness Unitarity ⇓ UV ProtectedGiven a HK the Slotheon is slower than the canonical cousin! Inflation
  46. 46. Introduction The New Higgs inflation is a Slotheonic theory Slow roll 1 G αβ The failure of LK = − g αβ − ∂α Φ∂β Φ Higgs boson 2 M2 New Higgs Inflation The name comes to the fact that on a given metric Gravitationally Enhanced Friction ˙ G tt ˙ Introducing the HK ∼ Φ 2 1 + 2 ≥ Φ2 Slotheon M Uniqueness Unitarity ⇓ UV ProtectedGiven a HK the Slotheon is slower than the canonical cousin! Inflation But this is another story...
  47. 47. Introduction Slow roll Uniqueness The failure of Higgs boson New HiggsWe found a realization of the ”New Higgs Inflation” idea Inflation Is this unique? Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  48. 48. Introduction Slow roll Uniqueness The failure of Higgs boson New HiggsWe found a realization of the ”New Higgs Inflation” idea Inflation Is this unique? Gravitationally Enhanced Friction Require only a spin-2 and a spin-0 degrees of freedom Introducing the to propagate (in general background) Slotheon Uniqueness Unitarity UV Protected Inflation
  49. 49. Introduction Slow roll Uniqueness The failure of Higgs boson New HiggsWe found a realization of the ”New Higgs Inflation” idea Inflation Is this unique? Gravitationally Enhanced Friction Require only a spin-2 and a spin-0 degrees of freedom Introducing the to propagate (in general background) Slotheon Uniqueness Modify only the kinetic term Unitarity UV Protected Inflation
  50. 50. Introduction Slow roll Uniqueness The failure of Higgs boson New HiggsWe found a realization of the ”New Higgs Inflation” idea Inflation Is this unique? Gravitationally Enhanced Friction Require only a spin-2 and a spin-0 degrees of freedom Introducing the to propagate (in general background) Slotheon Uniqueness Modify only the kinetic term Unitarity ⇓ UV Protected Inflation The unique action is the New Higgs Inflation action!!!
  51. 51. Proof: Introduction Slow roll The failure of Higgs boson New Higgs Inflation Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  52. 52. Proof: IntroductionBy Bianchi identities: δΦ G αβ ∂ α Φ∂β Φ → G αβ α βΦ Slow roll The failure ofNo higher derivatives! Higgs boson New Higgs Inflation Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  53. 53. Proof: IntroductionBy Bianchi identities: δΦ G αβ ∂ α Φ∂β Φ → G αβ α βΦ Slow roll The failure ofNo higher derivatives! Higgs bosonIn ADM language: no. of time derivatives in New Higgs InflationG αβ ∂α Φ∂β Φ never exceed the number of fields! Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  54. 54. Proof: IntroductionBy Bianchi identities: δΦ G αβ ∂ α Φ∂β Φ → G αβ α βΦ Slow roll The failure ofNo higher derivatives! Higgs bosonIn ADM language: no. of time derivatives in New Higgs InflationG αβ ∂α Φ∂β Φ never exceed the number of fields! Gravitationally Enhanced FrictionAny intercation with ˙ Φ2 (for example ˙ G tt Φ2 ) is Introducing the Slotheondangerous! (because of higher derivatives) Uniqueness Unitarity UV Protected Inflation
  55. 55. Proof: IntroductionBy Bianchi identities: δΦ G αβ ∂ α Φ∂β Φ → G αβ α βΦ Slow roll The failure ofNo higher derivatives! Higgs bosonIn ADM language: no. of time derivatives in New Higgs InflationG αβ ∂α Φ∂β Φ never exceed the number of fields! Gravitationally Enhanced FrictionAny intercation with ˙ Φ2 (for example ˙ G tt Φ2 ) is Introducing the Slotheondangerous! (because of higher derivatives) UniquenessHowever: G tt is special in ADM as it is the Hamiltonian Unitarityconstraint (only 1 derivative)! UV Protected Inflation
  56. 56. Proof: IntroductionBy Bianchi identities: δΦ G αβ ∂ α Φ∂β Φ → G αβ α βΦ Slow roll The failure ofNo higher derivatives! Higgs bosonIn ADM language: no. of time derivatives in New Higgs InflationG αβ ∂α Φ∂β Φ never exceed the number of fields! Gravitationally Enhanced FrictionAny intercation with ˙ Φ2(for example ˙ G tt Φ2 ) is Introducing the Slotheondangerous! (because of higher derivatives) UniquenessHowever: G tt is special in ADM as it is the Hamiltonian Unitarityconstraint (only 1 derivative)! UV Protected InflationN.B.: Any other curvature interaction would bring higherderivatives increasing the no. of propagating modes !!!
  57. 57. Proof: IntroductionBy Bianchi identities: δΦ G αβ ∂ α Φ∂β Φ → G αβ α βΦ Slow roll The failure ofNo higher derivatives! Higgs bosonIn ADM language: no. of time derivatives in New Higgs InflationG αβ ∂α Φ∂β Φ never exceed the number of fields! Gravitationally Enhanced FrictionAny intercation with ˙ Φ2(for example ˙ G tt Φ2 ) is Introducing the Slotheondangerous! (because of higher derivatives) UniquenessHowever: G tt is special in ADM as it is the Hamiltonian Unitarityconstraint (only 1 derivative)! UV Protected InflationN.B.: Any other curvature interaction would bring higherderivatives increasing the no. of propagating modes !!!In ADM language: Lapse and Shift are still Lagrangemultipliers → graviton propagates only 2 polarization
  58. 58. Unitarity Introduction Does the non-renormalizable operator Slow roll The failure of G αβ Higgs boson I = ∂α Φ∂β Φ M2 New Higgs Inflationviolates unitarity during Inflation since H 2 M 2? Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  59. 59. Unitarity Introduction Does the non-renormalizable operator Slow roll The failure of G αβ Higgs boson I = ∂α Φ∂β Φ M2 New Higgs Inflationviolates unitarity during Inflation since H 2 M 2? Gravitationally Enhanced Friction Check list: Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  60. 60. Unitarity Introduction Does the non-renormalizable operator Slow roll The failure of G αβ Higgs boson I = ∂α Φ∂β Φ M2 New Higgs Inflationviolates unitarity during Inflation since H 2 M 2? Gravitationally Enhanced Friction Check list: Introducing the SlotheonExpand the fields at linear level Uniqueness Unitarity UV Protected Inflation
  61. 61. Unitarity Introduction Does the non-renormalizable operator Slow roll The failure of G αβ Higgs boson I = ∂α Φ∂β Φ M2 New Higgs Inflation violates unitarity during Inflation since H 2 M 2? Gravitationally Enhanced Friction Check list: Introducing the SlotheonExpand the fields at linear level Uniqueness MCanonically normalize the Higgs: Φ = Φ0 + √ 3H φ Unitarity(the non-standard normalization comes from M −2 G tt φ2 ) ˙ UV Protected Inflation
  62. 62. Unitarity Introduction Does the non-renormalizable operator Slow roll The failure of G αβ Higgs boson I = ∂α Φ∂β Φ M2 New Higgs Inflation violates unitarity during Inflation since H 2 M 2? Gravitationally Enhanced Friction Check list: Introducing the SlotheonExpand the fields at linear level Uniqueness MCanonically normalize the Higgs: Φ = Φ0 + √ 3H φ Unitarity(the non-standard normalization comes from M −2 G tt φ2 ) ˙ UV Protected Inflation 0 1Canonically Normalize the metric: gµν = gµν + Mp hµν
  63. 63. Unitarity Introduction Does the non-renormalizable operator Slow roll The failure of G αβ Higgs boson I = ∂α Φ∂β Φ M2 New Higgs Inflation violates unitarity during Inflation since H 2 M 2? Gravitationally Enhanced Friction Check list: Introducing the SlotheonExpand the fields at linear level Uniqueness MCanonically normalize the Higgs: Φ = Φ0 + √ 3H φ Unitarity(the non-standard normalization comes from M −2 G tt φ2 ) ˙ UV Protected Inflation 0 1Canonically Normalize the metric: gµν = gµν + Mp hµνRead out the scale at which I ∼ O(1):No additional constraint than QG constraint H Mp !
  64. 64. Unitarity Introduction Does the non-renormalizable operator Slow roll The failure of G αβ Higgs boson I = ∂α Φ∂β Φ M2 New Higgs Inflation violates unitarity during Inflation since H 2 M 2? Gravitationally Enhanced Friction Check list: Introducing the Slotheon Expand the fields at linear level Uniqueness M Canonically normalize the Higgs: Φ = Φ0 + √ 3H φ Unitarity (the non-standard normalization comes from M −2 G tt φ2 ) ˙ UV Protected Inflation 0 1 Canonically Normalize the metric: gµν = gµν + Mp hµν Read out the scale at which I ∼ O(1): No additional constraint than QG constraint H Mp !Unitarity is not violated up to the Quantum Gravity scales!!!!
  65. 65. Introduction Slow rollUV Protected Inflation The failure of Higgs boson In large field scenarios New Higgs Inflation Φ Λcut−off Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  66. 66. Introduction Slow roll UV Protected Inflation The failure of Higgs boson In large field scenarios New Higgs Inflation Φ Λcut−off Gravitationally Enhanced Friction ⇓ Introducing the SlotheonThe (unknown) UV completed theory may spoil the effective UniquenessInflaton potential by higher powers of Φ2 /Λ2 cut−off , unless... Unitarity UV Protected Inflation
  67. 67. Introduction Slow roll UV Protected Inflation The failure of Higgs boson In large field scenarios New Higgs Inflation Φ Λcut−off Gravitationally Enhanced Friction ⇓ Introducing the SlotheonThe (unknown) UV completed theory may spoil the effective UniquenessInflaton potential by higher powers of Φ2 /Λ2 cut−off , unless... Unitarity UV Protected Inflation Some symmetries protect the potential
  68. 68. Suppose some global symmetry is broken at energies Introductionf >TeV (like in the QCD axion case) Slow roll The failure of Higgs boson New Higgs Inflation Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  69. 69. Suppose some global symmetry is broken at energies Introductionf >TeV (like in the QCD axion case) Slow rolla Pseudo Nambu-Goldstone Boson Φ is produced with a The failure of Higgs boson(one loop) potential New Higgs Inflation Φ2 2Λ4 1 − Gravitationally V (Φ) Enhanced Friction 4f 2 Introducing the Slotheonwhich is protected by the restoration of global shift Uniquenesssymmetry Φ → Φ + c at Λ → 0 Unitarity UV Protected Inflation
  70. 70. Suppose some global symmetry is broken at energies Introductionf >TeV (like in the QCD axion case) Slow rolla Pseudo Nambu-Goldstone Boson Φ is produced with a The failure of Higgs boson(one loop) potential New Higgs Inflation Φ2 2Λ4 1 − Gravitationally V (Φ) Enhanced Friction 4f 2 Introducing the Slotheonwhich is protected by the restoration of global shift Uniquenesssymmetry Φ → Φ + c at Λ → 0 UnitarityWith Λ Mp , Inflation predicts UV Protected Inflation M2 ns − 1 ∝ − 8πfp2
  71. 71. Suppose some global symmetry is broken at energies Introductionf >TeV (like in the QCD axion case) Slow rolla Pseudo Nambu-Goldstone Boson Φ is produced with a The failure of Higgs boson(one loop) potential New Higgs Inflation Φ2 2Λ4 1 − Gravitationally V (Φ) Enhanced Friction 4f 2 Introducing the Slotheonwhich is protected by the restoration of global shift Uniquenesssymmetry Φ → Φ + c at Λ → 0 UnitarityWith Λ Mp , Inflation predicts UV Protected Inflation M2 ns − 1 ∝ − 8πfp2so ns ≤ 1 → f > Mp ⇒ the model cannot be trusted!
  72. 72. Resolution IntroductionOnce again we can increase the friction so that Slow roll The failure of 2 Higgs boson old Mp → ⇒ ns − 1 ∼ − New Higgs Ω2 8πf Ω2 Inflation Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  73. 73. Resolution IntroductionOnce again we can increase the friction so that Slow roll The failure of 2 Higgs boson old Mp → ⇒ ns − 1 ∼ − New Higgs Ω2 8πf Ω2 Inflation Gravitationally Enhanced Friction Introducing the Then for large enough Ω, f Mp !!!! Slotheon Uniqueness The model is Natural!!! Unitarity UV Protected (i.e. no UV modifications of the potential) Inflation
  74. 74. Resolution Introduction Once again we can increase the friction so that Slow roll The failure of 2 Higgs boson old Mp → ⇒ ns − 1 ∼ − New Higgs Ω2 8πf Ω2 Inflation Gravitationally Enhanced Friction Introducing the Then for large enough Ω, f Mp !!!! Slotheon Uniqueness The model is Natural!!! Unitarity UV Protected (i.e. no UV modifications of the potential) InflationThe new coupling G αβ ∂α Φ∂β Φ is the unique that
  75. 75. Resolution Introduction Once again we can increase the friction so that Slow roll The failure of 2 Higgs boson old Mp → ⇒ ns − 1 ∼ − New Higgs Ω2 8πf Ω2 Inflation Gravitationally Enhanced Friction Introducing the Then for large enough Ω, f Mp !!!! Slotheon Uniqueness The model is Natural!!! Unitarity UV Protected (i.e. no UV modifications of the potential) InflationThe new coupling G αβ ∂α Φ∂β Φ is the unique thatDoes not introduce new degrees of freedom
  76. 76. Resolution Introduction Once again we can increase the friction so that Slow roll The failure of 2 Higgs boson old Mp → ⇒ ns − 1 ∼ − New Higgs Ω2 8πf Ω2 Inflation Gravitationally Enhanced Friction Introducing the Then for large enough Ω, f Mp !!!! Slotheon Uniqueness The model is Natural!!! Unitarity UV Protected (i.e. no UV modifications of the potential) InflationThe new coupling G αβ ∂α Φ∂β Φ is the unique thatDoes not introduce new degrees of freedomIs invariant under the global unbroken symmetryΦ→Φ+c
  77. 77. Introduction Slow roll Quantum gravity involvement to the one loop potential? The failure of Higgs boson New HiggsSince the symmetry is broken to a discrete group, Quantum Inflation gravity respect the symmetry Gravitationally Enhanced Friction ⇓ Introducing the Slotheon The only effect is to shift Λ → Λ0 + ΛQG Uniqueness Unitarity ⇓ UV Protected The form of the potential is unchanged, Λ fixed by Inflation observations!
  78. 78. Introduction Slow roll The failure of Higgs boson New Higgs Inflation Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected InflationHvala!

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