c. germani - sub-planckian higgs and axionic inflations
DESCRIPTION
The SEENET-MTP Workshop BW2011Particle Physics from TeV to Plank Scale28 August – 1 September 2011, Donji Milanovac, SerbiaTRANSCRIPT
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Sub-Planckian Higgs and Axionic Inflations
Cristiano GermaniBased on different collaborations: Martucci, Moyassari, Kehagias, Watanabe
LMU, ASC, Munich, Germany
BW2011, August 2011, Donji Milanovac, Serbia
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Introduction
Latest cosmological data agree impressively well with the aUniverse which is at large scales
homogeneous,
isotropic
spatially flat
A flat FRW Spacetime!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Introduction
Latest cosmological data agree impressively well with the aUniverse which is at large scales
homogeneous,
isotropic
spatially flat
A flat FRW Spacetime!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Introduction
Latest cosmological data agree impressively well with the aUniverse which is at large scales
homogeneous,
isotropic
spatially flat
A flat FRW Spacetime!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Introduction
Latest cosmological data agree impressively well with the aUniverse which is at large scales
homogeneous,
isotropic
spatially flat
A flat FRW Spacetime!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Introduction
Latest cosmological data agree impressively well with the aUniverse which is at large scales
homogeneous,
isotropic
spatially flat
A flat FRW Spacetime!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
A theoretical puzzle:
A flat FRW Universe
ds2 = −dt2 + a(t)2d~x · d~x
is extremely fine tuned solution of GR!
A simple idea to solve this puzzle is Inflation:
An exponential (accelerated and homogeneous) expansion ofthe Early Universe
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
A theoretical puzzle:
A flat FRW Universe
ds2 = −dt2 + a(t)2d~x · d~x
is extremely fine tuned solution of GR!
A simple idea to solve this puzzle is Inflation:
An exponential (accelerated and homogeneous) expansion ofthe Early Universe
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
By geometrical identities (Raychaudhuri equation)
a ∝ −( ρ︸︷︷︸effective energy density
+ 3 p︸︷︷︸effective pressure
)
⇓
ρ+ 3p < 0 , during inflationρ+ 3p > 0 , after inflation
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Slow Roll
A scalar field φ is a good candidate as
ρ =1
2φ2+V , p =
1
2φ2−V
⇓
ρ+ 3p ∝ φ2−V
⇓
φ2 V , Inflation happens (“slow roll”)φ2 ∼ V , Inflation ends
Q: Do we know any scalar field?
Higgs Boson!!!!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Slow Roll
A scalar field φ is a good candidate as
ρ =1
2φ2+V , p =
1
2φ2−V
⇓
ρ+ 3p ∝ φ2−V
⇓
φ2 V , Inflation happens (“slow roll”)φ2 ∼ V , Inflation ends
Q: Do we know any scalar field?
Higgs Boson!!!!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Slow Roll
A scalar field φ is a good candidate as
ρ =1
2φ2+V , p =
1
2φ2−V
⇓
ρ+ 3p ∝ φ2−V
⇓
φ2 V , Inflation happens (“slow roll”)φ2 ∼ V , Inflation ends
Q: Do we know any scalar field?
Higgs Boson!!!!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Slow Roll
A scalar field φ is a good candidate as
ρ =1
2φ2+V , p =
1
2φ2−V
⇓
ρ+ 3p ∝ φ2−V
⇓
φ2 V , Inflation happens (“slow roll”)φ2 ∼ V , Inflation ends
Q: Do we know any scalar field?
Higgs Boson!!!!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Slow Roll
A scalar field φ is a good candidate as
ρ =1
2φ2+V , p =
1
2φ2−V
⇓
ρ+ 3p ∝ φ2−V
⇓
φ2 V , Inflation happens (“slow roll”)φ2 ∼ V , Inflation ends
Q: Do we know any scalar field?
Higgs Boson!!!!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Slow Roll
A scalar field φ is a good candidate as
ρ =1
2φ2+V , p =
1
2φ2−V
⇓
ρ+ 3p ∝ φ2−V
⇓
φ2 V , Inflation happens (“slow roll”)φ2 ∼ V , Inflation ends
Q: Do we know any scalar field?
Higgs Boson!!!!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
The failure of Higgs boson in GR
The Higgs Lagrangian is
S =
∫d4x√−g
[M2
p R
2− DµH†DµH− λ
(H†H− v 2
)2]
All fields but H are subdominant during Inflation
Unitary gauge HT = (0, v+Φ√2
)
In order to slow roll Φ v
⇓
S =
∫d4x√−g
[R
2κ2− 1
2∂µΦ∂µΦ− λ
4Φ4
]
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
The failure of Higgs boson in GR
The Higgs Lagrangian is
S =
∫d4x√−g
[M2
p R
2− DµH†DµH− λ
(H†H− v 2
)2]
All fields but H are subdominant during Inflation
Unitary gauge HT = (0, v+Φ√2
)
In order to slow roll Φ v
⇓
S =
∫d4x√−g
[R
2κ2− 1
2∂µΦ∂µΦ− λ
4Φ4
]
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
The failure of Higgs boson in GR
The Higgs Lagrangian is
S =
∫d4x√−g
[M2
p R
2− DµH†DµH− λ
(H†H− v 2
)2]
All fields but H are subdominant during Inflation
Unitary gauge HT = (0, v+Φ√2
)
In order to slow roll Φ v
⇓
S =
∫d4x√−g
[R
2κ2− 1
2∂µΦ∂µΦ− λ
4Φ4
]
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
The failure of Higgs boson in GR
The Higgs Lagrangian is
S =
∫d4x√−g
[M2
p R
2− DµH†DµH− λ
(H†H− v 2
)2]
All fields but H are subdominant during Inflation
Unitary gauge HT = (0, v+Φ√2
)
In order to slow roll Φ v
⇓
S =
∫d4x√−g
[R
2κ2− 1
2∂µΦ∂µΦ− λ
4Φ4
]
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
The failure of Higgs boson in GR
The Higgs Lagrangian is
S =
∫d4x√−g
[M2
p R
2− DµH†DµH− λ
(H†H− v 2
)2]
All fields but H are subdominant during Inflation
Unitary gauge HT = (0, v+Φ√2
)
In order to slow roll Φ v
⇓
S =
∫d4x√−g
[R
2κ2− 1
2∂µΦ∂µΦ− λ
4Φ4
]
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Inflation:
H = a/a ' const (exponential expansion)
Φ 3HΦ (slow roll)
⇓
ε ≡ − HH2 1
⇓
Φ Mp !!!!
⇓
R M2p for the Standard Model values of λ ∼ 10−1 !
Inflation happens during the Quantum Gravity regime!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Inflation:
H = a/a ' const (exponential expansion)
Φ 3HΦ (slow roll)
⇓
ε ≡ − HH2 1
⇓
Φ Mp !!!!
⇓
R M2p for the Standard Model values of λ ∼ 10−1 !
Inflation happens during the Quantum Gravity regime!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Inflation:
H = a/a ' const (exponential expansion)
Φ 3HΦ (slow roll)
⇓
ε ≡ − HH2 1
⇓
Φ Mp !!!!
⇓
R M2p for the Standard Model values of λ ∼ 10−1 !
Inflation happens during the Quantum Gravity regime!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Inflation:
H = a/a ' const (exponential expansion)
Φ 3HΦ (slow roll)
⇓
ε ≡ − HH2 1
⇓
Φ Mp !!!!
⇓
R M2p for the Standard Model values of λ ∼ 10−1 !
Inflation happens during the Quantum Gravity regime!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Lowering the curvature during InflationRecapitulate:
R ∼ H2 ∝ V (Φ)
M2p
∝ Φ4
M2p
Φ ' −MpΦ
ε = − H
H2∝ Φ2
H2M2p
∼M2
p
Φ2 1⇒ Φ Mp
⇓
R M2p
Solution: Increase the friction!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Lowering the curvature during InflationRecapitulate:
R ∼ H2 ∝ V (Φ)
M2p
∝ Φ4
M2p
Φ ' −MpΦ
ε = − H
H2∝ Φ2
H2M2p
∼M2
p
Φ2 1⇒ Φ Mp
⇓
R M2p
Solution: Increase the friction!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Lowering the curvature during InflationRecapitulate:
R ∼ H2 ∝ V (Φ)
M2p
∝ Φ4
M2p
Φ ' −MpΦ
ε = − H
H2∝ Φ2
H2M2p
∼M2
p
Φ2 1⇒ Φ Mp
⇓
R M2p
Solution: Increase the friction!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Lowering the curvature during InflationRecapitulate:
R ∼ H2 ∝ V (Φ)
M2p
∝ Φ4
M2p
Φ ' −MpΦ
ε = − H
H2∝ Φ2
H2M2p
∼M2
p
Φ2 1⇒ Φ Mp
⇓
R M2p
Solution: Increase the friction!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Lowering the curvature during InflationRecapitulate:
R ∼ H2 ∝ V (Φ)
M2p
∝ Φ4
M2p
Φ ' −MpΦ
ε = − H
H2∝ Φ2
H2M2p
∼M2
p
Φ2 1⇒ Φ Mp
⇓
R M2p
Solution: Increase the friction!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
New Higgs Inflation
How to increase the friction:
if Φ→ Ω2Φ with Ω 1
then
ε ∝ Φ2
H2M2p
∼M2
p
Φ2Ω4 1→ M2
p R M2
p
Ω8(for large enough Ω)
Quantum Gravity regime is avoided during Inflation!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
New Higgs Inflation
How to increase the friction:
if Φ→ Ω2Φ with Ω 1
then
ε ∝ Φ2
H2M2p
∼M2
p
Φ2Ω4 1→ M2
p R M2
p
Ω8(for large enough Ω)
Quantum Gravity regime is avoided during Inflation!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
New Higgs Inflation
How to increase the friction:
if Φ→ Ω2Φ with Ω 1
then
ε ∝ Φ2
H2M2p
∼M2
p
Φ2Ω4 1→ M2
p R M2
p
Ω8(for large enough Ω)
Quantum Gravity regime is avoided during Inflation!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
New Higgs Inflation
How to increase the friction:
if Φ→ Ω2Φ with Ω 1
then
ε ∝ Φ2
H2M2p
∼M2
p
Φ2Ω4 1→ M2
p R M2
p
Ω8(for large enough Ω)
Quantum Gravity regime is avoided during Inflation!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
New Higgs Inflation
How to increase the friction:
if Φ→ Ω2Φ with Ω 1
then
ε ∝ Φ2
H2M2p
∼M2
p
Φ2Ω4 1→ M2
p R M2
p
Ω8(for large enough Ω)
Quantum Gravity regime is avoided during Inflation!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Gravitationally Enhanced Friction (GEF)
The friction should only be efficient at high energies:
Ω2 ∼ 3µH = f (H), dfdH ≥ 0
A typical (positive) enhancement could be
µ = 1 + H2
M2
If no new d.o.f. are added, the scalar e.o.m. can only be
µ(
Φ + 3HΦ)
= −V ′ → teff ' t√µ as µ
µH 1
If H M the scalar field clock is frozen w.r.t. the observerand friction is enhanced.
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Gravitationally Enhanced Friction (GEF)
The friction should only be efficient at high energies:
Ω2 ∼ 3µH = f (H), dfdH ≥ 0
A typical (positive) enhancement could be
µ = 1 + H2
M2
If no new d.o.f. are added, the scalar e.o.m. can only be
µ(
Φ + 3HΦ)
= −V ′ → teff ' t√µ as µ
µH 1
If H M the scalar field clock is frozen w.r.t. the observerand friction is enhanced.
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Gravitationally Enhanced Friction (GEF)
The friction should only be efficient at high energies:
Ω2 ∼ 3µH = f (H), dfdH ≥ 0
A typical (positive) enhancement could be
µ = 1 + H2
M2
If no new d.o.f. are added, the scalar e.o.m. can only be
µ(
Φ + 3HΦ)
= −V ′ → teff ' t√µ as µ
µH 1
If H M the scalar field clock is frozen w.r.t. the observerand friction is enhanced.
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Gravitationally Enhanced Friction (GEF)
The friction should only be efficient at high energies:
Ω2 ∼ 3µH = f (H), dfdH ≥ 0
A typical (positive) enhancement could be
µ = 1 + H2
M2
If no new d.o.f. are added, the scalar e.o.m. can only be
µ(
Φ + 3HΦ)
= −V ′ → teff ' t√µ as µ
µH 1
If H M the scalar field clock is frozen w.r.t. the observerand friction is enhanced.
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Gravitationally Enhanced Friction: Realization
We promote the rescaling to all coords.
∂µ →√µ∂µ, µ = 1 + H2
M2
Gαβ ' −H2gαβ during Inflation
gµν∂µΦ∂νΦ→(gµν − Gµν
M2
)∂µΦ∂νΦ
New Higgs Inflation Lagrangian
S =
∫d4x√−g
[R
2κ2− 1
2
(gαβ − Gαβ
M2
)∂αΦ∂βΦ− λ
4Φ4
]
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Gravitationally Enhanced Friction: Realization
We promote the rescaling to all coords.
∂µ →√µ∂µ, µ = 1 + H2
M2
Gαβ ' −H2gαβ during Inflation
gµν∂µΦ∂νΦ→(gµν − Gµν
M2
)∂µΦ∂νΦ
New Higgs Inflation Lagrangian
S =
∫d4x√−g
[R
2κ2− 1
2
(gαβ − Gαβ
M2
)∂αΦ∂βΦ− λ
4Φ4
]
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Gravitationally Enhanced Friction: Realization
We promote the rescaling to all coords.
∂µ →√µ∂µ, µ = 1 + H2
M2
Gαβ ' −H2gαβ during Inflation
gµν∂µΦ∂νΦ→(gµν − Gµν
M2
)∂µΦ∂νΦ
New Higgs Inflation Lagrangian
S =
∫d4x√−g
[R
2κ2− 1
2
(gαβ − Gαβ
M2
)∂αΦ∂βΦ− λ
4Φ4
]
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Gravitationally Enhanced Friction: Realization
We promote the rescaling to all coords.
∂µ →√µ∂µ, µ = 1 + H2
M2
Gαβ ' −H2gαβ during Inflation
gµν∂µΦ∂νΦ→(gµν − Gµν
M2
)∂µΦ∂νΦ
New Higgs Inflation Lagrangian
S =
∫d4x√−g
[R
2κ2− 1
2
(gαβ − Gαβ
M2
)∂αΦ∂βΦ− λ
4Φ4
]
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
The New Higgs inflation is a Slotheonic theory
LK = −1
2
(gαβ − Gαβ
M2
)∂αΦ∂βΦ
The name comes to the fact that on a given metric
HK ∼ Φ2
(1 +
G tt
M2
)≥ Φ2
⇓Given a HK the Slotheon is slower than the canonical cousin!
But this is another story...
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
The New Higgs inflation is a Slotheonic theory
LK = −1
2
(gαβ − Gαβ
M2
)∂αΦ∂βΦ
The name comes to the fact that on a given metric
HK ∼ Φ2
(1 +
G tt
M2
)≥ Φ2
⇓Given a HK the Slotheon is slower than the canonical cousin!
But this is another story...
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
The New Higgs inflation is a Slotheonic theory
LK = −1
2
(gαβ − Gαβ
M2
)∂αΦ∂βΦ
The name comes to the fact that on a given metric
HK ∼ Φ2
(1 +
G tt
M2
)≥ Φ2
⇓Given a HK the Slotheon is slower than the canonical cousin!
But this is another story...
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
The New Higgs inflation is a Slotheonic theory
LK = −1
2
(gαβ − Gαβ
M2
)∂αΦ∂βΦ
The name comes to the fact that on a given metric
HK ∼ Φ2
(1 +
G tt
M2
)≥ Φ2
⇓Given a HK the Slotheon is slower than the canonical cousin!
But this is another story...
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Uniqueness
We found a realization of the ”New Higgs Inflation” ideaIs this unique?
Require only a spin-2 and a spin-0 degrees of freedomto propagate (in general background)
Modify only the kinetic term
⇓
The unique action is the New Higgs Inflation action!!!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Uniqueness
We found a realization of the ”New Higgs Inflation” ideaIs this unique?
Require only a spin-2 and a spin-0 degrees of freedomto propagate (in general background)
Modify only the kinetic term
⇓
The unique action is the New Higgs Inflation action!!!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Uniqueness
We found a realization of the ”New Higgs Inflation” ideaIs this unique?
Require only a spin-2 and a spin-0 degrees of freedomto propagate (in general background)
Modify only the kinetic term
⇓
The unique action is the New Higgs Inflation action!!!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Uniqueness
We found a realization of the ”New Higgs Inflation” ideaIs this unique?
Require only a spin-2 and a spin-0 degrees of freedomto propagate (in general background)
Modify only the kinetic term
⇓
The unique action is the New Higgs Inflation action!!!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Proof:
By Bianchi identities: δΦGαβ∂αΦ∂βΦ→ Gαβ∇α∇βΦNo higher derivatives!
In ADM language: no. of time derivatives inGαβ∂αΦ∂βΦ never exceed the number of fields!
Any intercation with Φ2 (for example G ttΦ2) isdangerous! (because of higher derivatives)
However: G tt is special in ADM as it is the Hamiltonianconstraint (only 1 derivative)!N.B.: Any other curvature interaction would bring higher
derivatives increasing the no. of propagating modes !!!
In ADM language: Lapse and Shift are still Lagrangemultipliers → graviton propagates only 2 polarization
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Proof:
By Bianchi identities: δΦGαβ∂αΦ∂βΦ→ Gαβ∇α∇βΦNo higher derivatives!
In ADM language: no. of time derivatives inGαβ∂αΦ∂βΦ never exceed the number of fields!
Any intercation with Φ2 (for example G ttΦ2) isdangerous! (because of higher derivatives)
However: G tt is special in ADM as it is the Hamiltonianconstraint (only 1 derivative)!N.B.: Any other curvature interaction would bring higher
derivatives increasing the no. of propagating modes !!!
In ADM language: Lapse and Shift are still Lagrangemultipliers → graviton propagates only 2 polarization
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Proof:
By Bianchi identities: δΦGαβ∂αΦ∂βΦ→ Gαβ∇α∇βΦNo higher derivatives!
In ADM language: no. of time derivatives inGαβ∂αΦ∂βΦ never exceed the number of fields!
Any intercation with Φ2 (for example G ttΦ2) isdangerous! (because of higher derivatives)
However: G tt is special in ADM as it is the Hamiltonianconstraint (only 1 derivative)!N.B.: Any other curvature interaction would bring higher
derivatives increasing the no. of propagating modes !!!
In ADM language: Lapse and Shift are still Lagrangemultipliers → graviton propagates only 2 polarization
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Proof:
By Bianchi identities: δΦGαβ∂αΦ∂βΦ→ Gαβ∇α∇βΦNo higher derivatives!
In ADM language: no. of time derivatives inGαβ∂αΦ∂βΦ never exceed the number of fields!
Any intercation with Φ2 (for example G ttΦ2) isdangerous! (because of higher derivatives)
However: G tt is special in ADM as it is the Hamiltonianconstraint (only 1 derivative)!N.B.: Any other curvature interaction would bring higher
derivatives increasing the no. of propagating modes !!!
In ADM language: Lapse and Shift are still Lagrangemultipliers → graviton propagates only 2 polarization
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Proof:
By Bianchi identities: δΦGαβ∂αΦ∂βΦ→ Gαβ∇α∇βΦNo higher derivatives!
In ADM language: no. of time derivatives inGαβ∂αΦ∂βΦ never exceed the number of fields!
Any intercation with Φ2 (for example G ttΦ2) isdangerous! (because of higher derivatives)
However: G tt is special in ADM as it is the Hamiltonianconstraint (only 1 derivative)!
N.B.: Any other curvature interaction would bring higher
derivatives increasing the no. of propagating modes !!!
In ADM language: Lapse and Shift are still Lagrangemultipliers → graviton propagates only 2 polarization
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Proof:
By Bianchi identities: δΦGαβ∂αΦ∂βΦ→ Gαβ∇α∇βΦNo higher derivatives!
In ADM language: no. of time derivatives inGαβ∂αΦ∂βΦ never exceed the number of fields!
Any intercation with Φ2 (for example G ttΦ2) isdangerous! (because of higher derivatives)
However: G tt is special in ADM as it is the Hamiltonianconstraint (only 1 derivative)!N.B.: Any other curvature interaction would bring higher
derivatives increasing the no. of propagating modes !!!
In ADM language: Lapse and Shift are still Lagrangemultipliers → graviton propagates only 2 polarization
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Proof:
By Bianchi identities: δΦGαβ∂αΦ∂βΦ→ Gαβ∇α∇βΦNo higher derivatives!
In ADM language: no. of time derivatives inGαβ∂αΦ∂βΦ never exceed the number of fields!
Any intercation with Φ2 (for example G ttΦ2) isdangerous! (because of higher derivatives)
However: G tt is special in ADM as it is the Hamiltonianconstraint (only 1 derivative)!N.B.: Any other curvature interaction would bring higher
derivatives increasing the no. of propagating modes !!!
In ADM language: Lapse and Shift are still Lagrangemultipliers → graviton propagates only 2 polarization
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Unitarity
Does the non-renormalizable operator
I =Gαβ
M2∂αΦ∂βΦ
violates unitarity during Inflation since H2 M2?
Check list:
Expand the fields at linear level
Canonically normalize the Higgs: Φ = Φ0 + M√3Hφ
(the non-standard normalization comes from M−2G tt φ2)
Canonically Normalize the metric: gµν = g 0µν + 1
Mphµν
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
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Unitarity
Does the non-renormalizable operator
I =Gαβ
M2∂αΦ∂βΦ
violates unitarity during Inflation since H2 M2?Check list:
Expand the fields at linear level
Canonically normalize the Higgs: Φ = Φ0 + M√3Hφ
(the non-standard normalization comes from M−2G tt φ2)
Canonically Normalize the metric: gµν = g 0µν + 1
Mphµν
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
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Unitarity
Does the non-renormalizable operator
I =Gαβ
M2∂αΦ∂βΦ
violates unitarity during Inflation since H2 M2?Check list:
Expand the fields at linear level
Canonically normalize the Higgs: Φ = Φ0 + M√3Hφ
(the non-standard normalization comes from M−2G tt φ2)
Canonically Normalize the metric: gµν = g 0µν + 1
Mphµν
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
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Unitarity
Does the non-renormalizable operator
I =Gαβ
M2∂αΦ∂βΦ
violates unitarity during Inflation since H2 M2?Check list:
Expand the fields at linear level
Canonically normalize the Higgs: Φ = Φ0 + M√3Hφ
(the non-standard normalization comes from M−2G tt φ2)
Canonically Normalize the metric: gµν = g 0µν + 1
Mphµν
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
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Unitarity
Does the non-renormalizable operator
I =Gαβ
M2∂αΦ∂βΦ
violates unitarity during Inflation since H2 M2?Check list:
Expand the fields at linear level
Canonically normalize the Higgs: Φ = Φ0 + M√3Hφ
(the non-standard normalization comes from M−2G tt φ2)
Canonically Normalize the metric: gµν = g 0µν + 1
Mphµν
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
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Unitarity
Does the non-renormalizable operator
I =Gαβ
M2∂αΦ∂βΦ
violates unitarity during Inflation since H2 M2?Check list:
Expand the fields at linear level
Canonically normalize the Higgs: Φ = Φ0 + M√3Hφ
(the non-standard normalization comes from M−2G tt φ2)
Canonically Normalize the metric: gµν = g 0µν + 1
Mphµν
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
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Unitarity
Does the non-renormalizable operator
I =Gαβ
M2∂αΦ∂βΦ
violates unitarity during Inflation since H2 M2?Check list:
Expand the fields at linear level
Canonically normalize the Higgs: Φ = Φ0 + M√3Hφ
(the non-standard normalization comes from M−2G tt φ2)
Canonically Normalize the metric: gµν = g 0µν + 1
Mphµν
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
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
UV Protected Inflation
In large field scenariosΦ Λcut−off
⇓
The (unknown) UV completed theory may spoil the effectiveInflaton potential by higher powers of Φ2/Λ2
cut−off , unless...
Some symmetries protect the potential
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
UV Protected Inflation
In large field scenariosΦ Λcut−off
⇓
The (unknown) UV completed theory may spoil the effectiveInflaton potential by higher powers of Φ2/Λ2
cut−off , unless...
Some symmetries protect the potential
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
UV Protected Inflation
In large field scenariosΦ Λcut−off
⇓
The (unknown) UV completed theory may spoil the effectiveInflaton potential by higher powers of Φ2/Λ2
cut−off , unless...
Some symmetries protect the potential
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Suppose some global symmetry is broken at energiesf >TeV (like in the QCD axion case)
a Pseudo Nambu-Goldstone Boson Φ is produced with a(one loop) potential
V (Φ) ' 2Λ4
(1− Φ2
4f 2
)which is protected by the restoration of global shiftsymmetry Φ→ Φ + c at Λ→ 0
With Λ Mp, Inflation predicts
ns − 1 ∝ ε ' − M2p
8πf 2
so ns ≤ 1→ f > Mp ⇒ the model cannot be trusted!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Suppose some global symmetry is broken at energiesf >TeV (like in the QCD axion case)
a Pseudo Nambu-Goldstone Boson Φ is produced with a(one loop) potential
V (Φ) ' 2Λ4
(1− Φ2
4f 2
)which is protected by the restoration of global shiftsymmetry Φ→ Φ + c at Λ→ 0
With Λ Mp, Inflation predicts
ns − 1 ∝ ε ' − M2p
8πf 2
so ns ≤ 1→ f > Mp ⇒ the model cannot be trusted!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Suppose some global symmetry is broken at energiesf >TeV (like in the QCD axion case)
a Pseudo Nambu-Goldstone Boson Φ is produced with a(one loop) potential
V (Φ) ' 2Λ4
(1− Φ2
4f 2
)which is protected by the restoration of global shiftsymmetry Φ→ Φ + c at Λ→ 0
With Λ Mp, Inflation predicts
ns − 1 ∝ ε ' − M2p
8πf 2
so ns ≤ 1→ f > Mp ⇒ the model cannot be trusted!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Suppose some global symmetry is broken at energiesf >TeV (like in the QCD axion case)
a Pseudo Nambu-Goldstone Boson Φ is produced with a(one loop) potential
V (Φ) ' 2Λ4
(1− Φ2
4f 2
)which is protected by the restoration of global shiftsymmetry Φ→ Φ + c at Λ→ 0
With Λ Mp, Inflation predicts
ns − 1 ∝ ε ' − M2p
8πf 2
so ns ≤ 1→ f > Mp ⇒ the model cannot be trusted!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Resolution
Once again we can increase the friction so that
ε→ εold
Ω2⇒ ns − 1 ∼ −
M2p
8πf Ω2
Then for large enough Ω, f Mp!!!!
The model is Natural!!!(i.e. no UV modifications of the potential)
The new coupling Gαβ∂αΦ∂βΦ is the unique that
Does not introduce new degrees of freedom
Is invariant under the global unbroken symmetryΦ→ Φ + c
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Resolution
Once again we can increase the friction so that
ε→ εold
Ω2⇒ ns − 1 ∼ −
M2p
8πf Ω2
Then for large enough Ω, f Mp!!!!
The model is Natural!!!(i.e. no UV modifications of the potential)
The new coupling Gαβ∂αΦ∂βΦ is the unique that
Does not introduce new degrees of freedom
Is invariant under the global unbroken symmetryΦ→ Φ + c
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Resolution
Once again we can increase the friction so that
ε→ εold
Ω2⇒ ns − 1 ∼ −
M2p
8πf Ω2
Then for large enough Ω, f Mp!!!!
The model is Natural!!!(i.e. no UV modifications of the potential)
The new coupling Gαβ∂αΦ∂βΦ is the unique that
Does not introduce new degrees of freedom
Is invariant under the global unbroken symmetryΦ→ Φ + c
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Resolution
Once again we can increase the friction so that
ε→ εold
Ω2⇒ ns − 1 ∼ −
M2p
8πf Ω2
Then for large enough Ω, f Mp!!!!
The model is Natural!!!(i.e. no UV modifications of the potential)
The new coupling Gαβ∂αΦ∂βΦ is the unique that
Does not introduce new degrees of freedom
Is invariant under the global unbroken symmetryΦ→ Φ + c
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Resolution
Once again we can increase the friction so that
ε→ εold
Ω2⇒ ns − 1 ∼ −
M2p
8πf Ω2
Then for large enough Ω, f Mp!!!!
The model is Natural!!!(i.e. no UV modifications of the potential)
The new coupling Gαβ∂αΦ∂βΦ is the unique that
Does not introduce new degrees of freedom
Is invariant under the global unbroken symmetryΦ→ Φ + c
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Quantum gravity involvement to the one loop potential?
Since the symmetry is broken to a discrete group, Quantumgravity respect the symmetry
⇓The only effect is to shift Λ→ Λ0 + ΛQG
⇓The form of the potential is unchanged, Λ fixed by
observations!
Introduction
Slow roll
The failure ofHiggs boson
New HiggsInflation
GravitationallyEnhanced Friction
Introducing theSlotheon
Uniqueness
Unitarity
UV ProtectedInflation
Hvala!