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!