Gravity as the Origin of Spontaneous Symmetry Breaking in the - - PowerPoint PPT Presentation

Gravity as the Origin of Spontaneous Symmetry Breaking in the Inflationary Universe

Research Center for the Early Universe (RESCEU), Univ. of Tokyo Yuki Watanabe arXiv: 12xx.xxxx Work in progress with F. Bezrukov PRD83, 043511 (2011) PRD75, 061301(R) (2007) with E. Komatsu

The Inflationary Universe

• Inflation solves flatness, horizon, monopole problems
• f the big bang theory.
• At the same time, it provides the initial seed of

density fluctuations that develop to cosmic structures like galaxies. Since the density fluctuations come from quantum vacuum fluctuations, they obey Gaussian statistics.

• From observations of CMB temperature anisotropy,

the amplitude and tilt of the power-spectrum are given by Pζ ~ 10-9, ns ~ 0.96. It is consistent with Gaussian fluctuations: -10 < fNL < 74.

The Standard Model Higgs

• The SM of elementary particles is composed of

quarks, leptons, neutrinos, gauge bosons, and Higgs boson.

• The vev of Higgs gives rise to mass to all particles

except photons, gluons, and neutrinos.

• From experiments of LHC, the SM Higgs seems to

be detected. ATLAS: m ~ 126.5 GeV (5σ); CMS: m ~ 125.3 ± 0.6 GeV (4.9σ)

Is the inflaton Higgs?

• No, if gravity is minimally coupled to the Higgs.

Pζ ~ 104 λ ~ 102 too big!

• Yes, if gravity is non-minimally coupled to the Higgs.

[Futamase & Maeda 89; Komatsu & Futamase 99; Bezrukov & Shaposhnikov 08; Barbinsky, Kamenshchik & Starobinsky 08; Germani & Kehagias 10; Germani & YW 11; Kamada, Kobayashi, Yamaguchi & Yokoyama 12; ...]

Pζ ~ λ/ξ2 ~ 10-9 for ξ ~ 5x103

• How to reheat the Universe? [YW & Komatsu 07; Bezrukov,

Gorbunov & Shaposhnikov 09; Garcia-Bellido et al 09; YW 11]

Is the inflaton Higgs?

• No, if gravity is minimally coupled to the Higgs.

Pζ ~ 104 λ ~ 102 too big!

• Yes, if gravity is non-minimally coupled to the Higgs.

[Futamase & Maeda 89; Komatsu & Futamase 99; Bezrukov & Shaposhnikov 08; Barbinsky, Kamenshchik & Starobinsky 08; Germani & Kehagias 10; Germani & YW 11; Kamada, Kobayashi, Yamaguchi & Yokoyama 12; ...]

Pζ ~ 10-4 λM2/H2 ~ 10-9 for H/M ~ 50

• How to reheat the Universe? [YW & Komatsu 07; Bezrukov,

Gorbunov & Shaposhnikov 09; Garcia-Bellido et al 09; YW 11]

Is the inflaton Higgs?

• No, if gravity is minimally coupled to the Higgs.

Pζ ~ 104 λ ~ 102 too big!

• Yes, if gravity is non-minimally coupled to the Higgs.

[Futamase & Maeda 89; Komatsu & Futamase 99; Bezrukov & Shaposhnikov 08; Barbinsky, Kamenshchik & Starobinsky 08; Germani & Kehagias 10; Germani & YW 11; Kamada, Kobayashi, Yamaguchi & Yokoyama 12; ...]

Pζ ~ λ/ξ2 ~ 10-9 for ξ ~ 5x103

• How to reheat the Universe? → gravitational

inflaton decay [YW & Komatsu 07; 08; Bezrukov, Gorbunov &

Shaposhnikov 09; Garcia-Bellido et al 09; YW 11]

SM Higgs as the inflaton

• SM Higgs inflation [Bezrukov & Shaposhnikov 08; Barbinsky,

Kamenshchik & Starobinsky 08; ...]

• Minimalistic to explain both CMB spectra and LHC

data

• Higgs gives masses to gauge bosons and quarks. →

Parametric resonance of W, Z happens during

• scillations and reheats the Universe [Bezrukov, Gorbunov &

Shaposhnikov 09; Garcia-Bellido et al 09]

Meta-stability of SM vacuum at high energy?

[J. Elias-Miro et al 12]

• RG running of λ is sensitive to top mass and strong

coupling constant.

• Need additional d.o.f? Bosons change the running of λ

positively while fermions do it negatively.

Instability 106 107 108 109 1010 1012 1014 1016 110 115 120 125 130 135 140 165 170 175 180 Higgs mass mh in GeV Pole top mass mt in GeV Instability Stability Meta-stability

102 104 106 108 1010 1012 1014 1016 1018 1020

• 0.06
• 0.04
• 0.02

0.00 0.02 0.04 0.06 RGE scale m in GeV Higgs quartic coupling lHmL

mh = 126 GeV

mt = 173.2 GeV a3HMZL = 0.1184 mt = 171.4 GeV a3HMZL = 0.117 a3HMZL = 0.1198 mt = 175. GeV

Any other classical condensates during Higgs inflation?

• Scalar condensate:
• Heavy → integrated out; It may leave features on CMB

spectra.

• Light → frozen but affect inflationary dynamics later; It may

become Dark Matter (if stable) after inflation.

• Vector condensate → anisotropy [M. Watanabe, Kanno & Soda

09; ...]

• Can they be curvatons?
• Do they change dynamics and reheating process?

“Spontaneous symmetry breakdown” due to gravity

• Light scalar dominates energy density after inflation. → Higgs

acquires non-trivial vev due to negative mass term. It diminishes the amplitude of Higgs oscillations, and reheating proceeds perturbatively.

h Φ V

• Decay channels: Φ, W, Z, top → kinematically allowed?

If not, Higgs decays mainly into Φ (tree), γ, gluon (loop)

• gravitationally. [YW 11]
• Light scalars become Dark Matter if they are stable. If

unstable, they must decay before BBN.

Reheating with light scalar condensates

Gravitational inflaton decay [YW 11]

gµν (x) → ˆ g

µν (x) = Ω2(x)gµν (x)

≈ gµν + gµν F(v)σ MPl

2

Tm

µ µ[ˆ

g

µν ] = − Ω

−ˆ g δSm[ˆ g

µν ]

δΩ

Conformal invariance: local scale invariance Mass term explicitly breaks scale invariance.

Conformal invariant field:

• Massless spin-½ fields
• Conformally coupled massless spin-0 fields
• Gauge fields (classical level)

A A g g ψ ψ

at the classical level

Lint = √−g F1(v)σ 2M 2

P l

T µ

mµ

T µ

mµ = Nχ

• s=1

2 [−(Dµχs)∗Dµχs + 2U(χ∗

sχs)] + Nψ

• f=1

mf ¯ ψfψf + βh(g) 2g FµνF µν

Gauge trace anomaly: lowest order decay channel to photons

two-photon decay of the Higgs

Summery of decay rates

Femions Scalars Gauge fields Probably most efficient.

Γ(σ χ+χ−) Nχ[F1(v)]2m3

σ

64πM 4

P l

Γ(σ ¯ ψψ) Nψ[F1(v)]2mσm2

ψ

32πM 4

P l

Γ(σ → 2Aµ) = α2[F1(v)]2m3

σ

1024π3M 4

Pl

• Nψ
• f=1

2If

• m2

σ

m2

f

• +

Nχ

• s=1
• 2 + m2

σ

m2

s

• Is

m2

σ

m2

s

• 2

Preheating with light scalar condensates?

• Gravitationally induced couplings cannot be so

large since they are essentially Planck-suppressed.

• Direct couplings to the scalar are assumed to be
• small. Of course, yes in principle.

Conclusions and future work...

• SM Higgs inflation can be saved by additional scalars.
• However, SSB due to gravity may occur after inflation if

the scalar dominates energy density.

• Reheating occurs naturally.
• Works left: Dark Matter abundance, Baryogenesis, ...