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C. Germani - Sub-Planckian Higgs and Axionic Inflations

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SEENET-MTP
SEENET-MTP

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

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Introduction Slow roll The failure of Higgs boson Sub-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
Introduction Introduction Slow roll Latest 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
Introduction Introduction Slow roll Latest 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
Introduction Introduction Slow roll Latest 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
Introduction Introduction Slow roll Latest 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
Introduction Introduction Slow roll Latest 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!
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 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
Introduction Slow roll The failure of By 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
Slow Roll Introduction A 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
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 Slotheon Uniqueness Unitarity UV Protected Inflation
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
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 ˙2 φ V , Inflation happens (“slow roll”) ˙ φ2 ∼ V , Inflation ends
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 ˙2 φ V , Inflation happens (“slow roll”) ˙ φ2 ∼ V , Inflation ends Q: Do we know any scalar field?
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 ˙2 φ V , Inflation happens (“slow roll”) ˙ φ2 ∼ V , Inflation ends Q: Do we know any scalar field? Higgs Boson!!!!
The failure of Higgs boson in GR Introduction Slow roll The Higgs Lagrangian is The failure of Higgs boson 2 √ Mp R 2 New Higgs S= 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
The failure of Higgs boson in GR Introduction Slow roll The Higgs Lagrangian is The failure of Higgs boson 2 √ Mp R 2 New Higgs S= 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
The failure of Higgs boson in GR Introduction Slow roll The Higgs Lagrangian is The failure of Higgs boson 2 √ Mp R 2 New Higgs S= 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
The failure of Higgs boson in GR Introduction Slow roll The Higgs Lagrangian is The failure of Higgs boson 2 √ Mp R 2 New Higgs S= 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
The failure of Higgs boson in GR Introduction Slow roll The Higgs Lagrangian is The failure of Higgs boson 2 √ Mp R 2 New Higgs S= 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
Inflation: Introduction H = 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
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 UV Protected Inflation
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
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 ! 2 Inflation happens during the Quantum Gravity regime!
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
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
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
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
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!
Introduction New Higgs Inflation Slow roll The failure of Higgs boson How to increase the friction: New Higgs Inflation Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
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 Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
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 Uniqueness Unitarity UV Protected Inflation
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
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!
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 Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
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 Unitarity UV Protected Inflation
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 Inflation
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 Inflation If H M the scalar field clock is frozen w.r.t. the observer and friction is enhanced.
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 Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
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 Uniqueness Unitarity UV Protected Inflation
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 Inflation
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 4 S= d 4 x −g 2 − g αβ − ∂α Φ∂β Φ − Φ 2κ 2 M2 4
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 Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
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 Protected Inflation
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 Protected Given a HK the Slotheon is slower than the canonical cousin! Inflation
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 Protected Given a HK the Slotheon is slower than the canonical cousin! Inflation But this is another story...
Introduction Slow roll Uniqueness The failure of Higgs boson New Higgs We found a realization of the ”New Higgs Inflation” idea Inflation Is this unique? Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
Introduction Slow roll Uniqueness The failure of Higgs boson New Higgs We 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
Introduction Slow roll Uniqueness The failure of Higgs boson New Higgs We 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
Introduction Slow roll Uniqueness The failure of Higgs boson New Higgs We 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!!!
Proof: Introduction Slow roll The failure of Higgs boson New Higgs Inflation Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
Proof: Introduction By Bianchi identities: δΦ G αβ ∂ α Φ∂β Φ → G αβ α βΦ Slow roll The failure of No higher derivatives! Higgs boson New Higgs Inflation Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
Proof: Introduction By Bianchi identities: δΦ G αβ ∂ α Φ∂β Φ → G αβ α βΦ Slow roll The failure of No higher derivatives! Higgs boson In ADM language: no. of time derivatives in New Higgs Inflation G αβ ∂α Φ∂β Φ never exceed the number of fields! Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
Proof: Introduction By Bianchi identities: δΦ G αβ ∂ α Φ∂β Φ → G αβ α βΦ Slow roll The failure of No higher derivatives! Higgs boson In ADM language: no. of time derivatives in New Higgs Inflation G αβ ∂α Φ∂β Φ never exceed the number of fields! Gravitationally Enhanced Friction Any intercation with ˙ Φ2 (for example ˙ G tt Φ2 ) is Introducing the Slotheon dangerous! (because of higher derivatives) Uniqueness Unitarity UV Protected Inflation
Proof: Introduction By Bianchi identities: δΦ G αβ ∂ α Φ∂β Φ → G αβ α βΦ Slow roll The failure of No higher derivatives! Higgs boson In ADM language: no. of time derivatives in New Higgs Inflation G αβ ∂α Φ∂β Φ never exceed the number of fields! Gravitationally Enhanced Friction Any intercation with ˙ Φ2 (for example ˙ G tt Φ2 ) is Introducing the Slotheon dangerous! (because of higher derivatives) Uniqueness However: G tt is special in ADM as it is the Hamiltonian Unitarity constraint (only 1 derivative)! UV Protected Inflation
Proof: Introduction By Bianchi identities: δΦ G αβ ∂ α Φ∂β Φ → G αβ α βΦ Slow roll The failure of No higher derivatives! Higgs boson In ADM language: no. of time derivatives in New Higgs Inflation G αβ ∂α Φ∂β Φ never exceed the number of fields! Gravitationally Enhanced Friction Any intercation with ˙ Φ2(for example ˙ G tt Φ2 ) is Introducing the Slotheon dangerous! (because of higher derivatives) Uniqueness However: G tt is special in ADM as it is the Hamiltonian Unitarity constraint (only 1 derivative)! UV Protected Inflation N.B.: Any other curvature interaction would bring higher derivatives increasing the no. of propagating modes !!!
Proof: Introduction By Bianchi identities: δΦ G αβ ∂ α Φ∂β Φ → G αβ α βΦ Slow roll The failure of No higher derivatives! Higgs boson In ADM language: no. of time derivatives in New Higgs Inflation G αβ ∂α Φ∂β Φ never exceed the number of fields! Gravitationally Enhanced Friction Any intercation with ˙ Φ2(for example ˙ G tt Φ2 ) is Introducing the Slotheon dangerous! (because of higher derivatives) Uniqueness However: G tt is special in ADM as it is the Hamiltonian Unitarity constraint (only 1 derivative)! UV Protected Inflation N.B.: Any other curvature interaction would bring higher derivatives increasing the no. of propagating modes !!! In ADM language: Lapse and Shift are still Lagrange multipliers → graviton propagates only 2 polarization
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 Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
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 Uniqueness Unitarity UV Protected Inflation
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 Unitarity UV Protected Inflation
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
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
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 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!!!!
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 Slotheon Uniqueness Unitarity UV Protected Inflation
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 Slotheon The (unknown) UV completed theory may spoil the effective Uniqueness Inflaton potential by higher powers of Φ2 /Λ2 cut−off , unless... Unitarity UV Protected Inflation
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 Slotheon The (unknown) UV completed theory may spoil the effective Uniqueness Inflaton potential by higher powers of Φ2 /Λ2 cut−off , unless... Unitarity UV Protected Inflation Some symmetries protect the potential
Suppose some global symmetry is broken at energies Introduction f >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
Suppose some global symmetry is broken at energies Introduction f >TeV (like in the QCD axion case) Slow roll a 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 Slotheon which is protected by the restoration of global shift Uniqueness symmetry Φ → Φ + c at Λ → 0 Unitarity UV Protected Inflation
Suppose some global symmetry is broken at energies Introduction f >TeV (like in the QCD axion case) Slow roll a 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 Slotheon which is protected by the restoration of global shift Uniqueness symmetry Φ → Φ + c at Λ → 0 Unitarity With Λ Mp , Inflation predicts UV Protected Inflation M2 ns − 1 ∝ − 8πfp2
Suppose some global symmetry is broken at energies Introduction f >TeV (like in the QCD axion case) Slow roll a 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 Slotheon which is protected by the restoration of global shift Uniqueness symmetry Φ → Φ + c at Λ → 0 Unitarity With Λ Mp , Inflation predicts UV Protected Inflation M2 ns − 1 ∝ − 8πfp2 so ns ≤ 1 → f > Mp ⇒ the model cannot be trusted!
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 Slotheon Uniqueness Unitarity UV Protected Inflation
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) Inflation
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) Inflation The new coupling G αβ ∂α Φ∂β Φ is the unique that
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) Inflation The new coupling G αβ ∂α Φ∂β Φ is the unique that Does not introduce new degrees of freedom
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) Inflation The new coupling G αβ ∂α Φ∂β Φ is the unique that Does not introduce new degrees of freedom Is invariant under the global unbroken symmetry Φ→Φ+c
Introduction Slow roll Quantum gravity involvement to the one loop potential? The failure of Higgs boson New Higgs Since 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!
Introduction Slow roll The failure of Higgs boson New Higgs Inflation Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation Hvala!

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C. Germani - Sub-Planckian Higgs and Axionic Inflations

  • 1. Introduction Slow roll The failure of Higgs boson Sub-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. Introduction Introduction Slow roll Latest 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. Introduction Introduction Slow roll Latest 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. Introduction Introduction Slow roll Latest 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. Introduction Introduction Slow roll Latest 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. Introduction Introduction Slow roll Latest 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. 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
  • 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. Introduction Slow roll The failure of By 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. Slow Roll Introduction A 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. 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 Slotheon Uniqueness Unitarity UV Protected Inflation
  • 12. 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
  • 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 ˙2 φ V , Inflation happens (“slow roll”) ˙ φ2 ∼ V , Inflation ends
  • 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 ˙2 φ V , Inflation happens (“slow roll”) ˙ φ2 ∼ V , Inflation ends Q: Do we know any scalar field?
  • 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 ˙2 φ V , Inflation happens (“slow roll”) ˙ φ2 ∼ V , Inflation ends Q: Do we know any scalar field? Higgs Boson!!!!
  • 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 Higgs S= 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. The failure of Higgs boson in GR Introduction Slow roll The Higgs Lagrangian is The failure of Higgs boson 2 √ Mp R 2 New Higgs S= 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. The failure of Higgs boson in GR Introduction Slow roll The Higgs Lagrangian is The failure of Higgs boson 2 √ Mp R 2 New Higgs S= 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. The failure of Higgs boson in GR Introduction Slow roll The Higgs Lagrangian is The failure of Higgs boson 2 √ Mp R 2 New Higgs S= 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. The failure of Higgs boson in GR Introduction Slow roll The Higgs Lagrangian is The failure of Higgs boson 2 √ Mp R 2 New Higgs S= 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. Inflation: Introduction H = 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. 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 UV Protected Inflation
  • 23. 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
  • 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 ! 2 Inflation happens during the Quantum Gravity regime!
  • 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. 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. 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. 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. 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. Introduction New Higgs Inflation Slow roll The failure of Higgs boson How to increase the friction: New Higgs Inflation Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  • 31. 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 Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  • 32. 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 Uniqueness Unitarity UV Protected Inflation
  • 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. 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. 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 Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  • 36. 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 Unitarity UV Protected Inflation
  • 37. 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 Inflation
  • 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 Inflation If H M the scalar field clock is frozen w.r.t. the observer and friction is enhanced.
  • 39. 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 Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  • 40. 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 Uniqueness Unitarity UV Protected Inflation
  • 41. 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 Inflation
  • 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 4 S= d 4 x −g 2 − g αβ − ∂α Φ∂β Φ − Φ 2κ 2 M2 4
  • 43. 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 Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  • 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 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 Protected Inflation
  • 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 Protected Given a HK the Slotheon is slower than the canonical cousin! Inflation
  • 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 Protected Given a HK the Slotheon is slower than the canonical cousin! Inflation But this is another story...
  • 47. Introduction Slow roll Uniqueness The failure of Higgs boson New Higgs We 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. Introduction Slow roll Uniqueness The failure of Higgs boson New Higgs We 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. Introduction Slow roll Uniqueness The failure of Higgs boson New Higgs We 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. Introduction Slow roll Uniqueness The failure of Higgs boson New Higgs We 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. Proof: Introduction Slow roll The failure of Higgs boson New Higgs Inflation Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  • 52. Proof: Introduction By Bianchi identities: δΦ G αβ ∂ α Φ∂β Φ → G αβ α βΦ Slow roll The failure of No higher derivatives! Higgs boson New Higgs Inflation Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  • 53. Proof: Introduction By Bianchi identities: δΦ G αβ ∂ α Φ∂β Φ → G αβ α βΦ Slow roll The failure of No higher derivatives! Higgs boson In ADM language: no. of time derivatives in New Higgs Inflation G αβ ∂α Φ∂β Φ never exceed the number of fields! Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  • 54. Proof: Introduction By Bianchi identities: δΦ G αβ ∂ α Φ∂β Φ → G αβ α βΦ Slow roll The failure of No higher derivatives! Higgs boson In ADM language: no. of time derivatives in New Higgs Inflation G αβ ∂α Φ∂β Φ never exceed the number of fields! Gravitationally Enhanced Friction Any intercation with ˙ Φ2 (for example ˙ G tt Φ2 ) is Introducing the Slotheon dangerous! (because of higher derivatives) Uniqueness Unitarity UV Protected Inflation
  • 55. Proof: Introduction By Bianchi identities: δΦ G αβ ∂ α Φ∂β Φ → G αβ α βΦ Slow roll The failure of No higher derivatives! Higgs boson In ADM language: no. of time derivatives in New Higgs Inflation G αβ ∂α Φ∂β Φ never exceed the number of fields! Gravitationally Enhanced Friction Any intercation with ˙ Φ2 (for example ˙ G tt Φ2 ) is Introducing the Slotheon dangerous! (because of higher derivatives) Uniqueness However: G tt is special in ADM as it is the Hamiltonian Unitarity constraint (only 1 derivative)! UV Protected Inflation
  • 56. Proof: Introduction By Bianchi identities: δΦ G αβ ∂ α Φ∂β Φ → G αβ α βΦ Slow roll The failure of No higher derivatives! Higgs boson In ADM language: no. of time derivatives in New Higgs Inflation G αβ ∂α Φ∂β Φ never exceed the number of fields! Gravitationally Enhanced Friction Any intercation with ˙ Φ2(for example ˙ G tt Φ2 ) is Introducing the Slotheon dangerous! (because of higher derivatives) Uniqueness However: G tt is special in ADM as it is the Hamiltonian Unitarity constraint (only 1 derivative)! UV Protected Inflation N.B.: Any other curvature interaction would bring higher derivatives increasing the no. of propagating modes !!!
  • 57. Proof: Introduction By Bianchi identities: δΦ G αβ ∂ α Φ∂β Φ → G αβ α βΦ Slow roll The failure of No higher derivatives! Higgs boson In ADM language: no. of time derivatives in New Higgs Inflation G αβ ∂α Φ∂β Φ never exceed the number of fields! Gravitationally Enhanced Friction Any intercation with ˙ Φ2(for example ˙ G tt Φ2 ) is Introducing the Slotheon dangerous! (because of higher derivatives) Uniqueness However: G tt is special in ADM as it is the Hamiltonian Unitarity constraint (only 1 derivative)! UV Protected Inflation N.B.: Any other curvature interaction would bring higher derivatives increasing the no. of propagating modes !!! In ADM language: Lapse and Shift are still Lagrange multipliers → graviton propagates only 2 polarization
  • 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 Inflation violates unitarity during Inflation since H 2 M 2? Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  • 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 Inflation violates unitarity during Inflation since H 2 M 2? Gravitationally Enhanced Friction Check list: Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation
  • 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 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 Unitarity UV Protected Inflation
  • 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 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
  • 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 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
  • 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 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 !
  • 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. 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 Slotheon Uniqueness Unitarity UV Protected Inflation
  • 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 Slotheon The (unknown) UV completed theory may spoil the effective Uniqueness Inflaton potential by higher powers of Φ2 /Λ2 cut−off , unless... Unitarity UV Protected Inflation
  • 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 Slotheon The (unknown) UV completed theory may spoil the effective Uniqueness Inflaton potential by higher powers of Φ2 /Λ2 cut−off , unless... Unitarity UV Protected Inflation Some symmetries protect the potential
  • 68. Suppose some global symmetry is broken at energies Introduction f >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. Suppose some global symmetry is broken at energies Introduction f >TeV (like in the QCD axion case) Slow roll a 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 Slotheon which is protected by the restoration of global shift Uniqueness symmetry Φ → Φ + c at Λ → 0 Unitarity UV Protected Inflation
  • 70. Suppose some global symmetry is broken at energies Introduction f >TeV (like in the QCD axion case) Slow roll a 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 Slotheon which is protected by the restoration of global shift Uniqueness symmetry Φ → Φ + c at Λ → 0 Unitarity With Λ Mp , Inflation predicts UV Protected Inflation M2 ns − 1 ∝ − 8πfp2
  • 71. Suppose some global symmetry is broken at energies Introduction f >TeV (like in the QCD axion case) Slow roll a 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 Slotheon which is protected by the restoration of global shift Uniqueness symmetry Φ → Φ + c at Λ → 0 Unitarity With Λ Mp , Inflation predicts UV Protected Inflation M2 ns − 1 ∝ − 8πfp2 so ns ≤ 1 → f > Mp ⇒ the model cannot be trusted!
  • 72. 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 Slotheon Uniqueness Unitarity UV Protected Inflation
  • 73. 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) Inflation
  • 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) Inflation The new coupling G αβ ∂α Φ∂β Φ is the unique that
  • 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) Inflation The new coupling G αβ ∂α Φ∂β Φ is the unique that Does not introduce new degrees of freedom
  • 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) Inflation The new coupling G αβ ∂α Φ∂β Φ is the unique that Does not introduce new degrees of freedom Is invariant under the global unbroken symmetry Φ→Φ+c
  • 77. Introduction Slow roll Quantum gravity involvement to the one loop potential? The failure of Higgs boson New Higgs Since 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. Introduction Slow roll The failure of Higgs boson New Higgs Inflation Gravitationally Enhanced Friction Introducing the Slotheon Uniqueness Unitarity UV Protected Inflation Hvala!