Gravity as the Origin of Spontaneous Symmetry Breaking in the Inflationary

UniverseResearch Center for the Early Universe (RESCEU), Univ. of Tokyo

Yuki Watanabe

arXiv: 12xx.xxxxWork in progress with F. Bezrukov

PRD83, 043511 (2011)PRD75, 061301(R) (2007) with E. Komatsu

The Inflationary Universe

• Inflation solves flatness, horizon, monopole problems of 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 oscillations 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.

Instability106 107 108 109 1010

1012

10141016

110 115 120 125 130 135 140165

170

175

180

Higgs mass mh in GeV

Poletopmassm

tinGeV

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

HiggsquarticcouplinglHmL

mh = 126 GeV

mt = 173.2 GeVa3HMZL = 0.1184

mt = 171.4 GeV

a3HMZL = 0.117a3HMZL = 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)σMPl

2

€

Tmµ

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)

AA

g gψ

ψ

at the classical level

Lint =⇥�g

F1(v)⇥2M2

Pl

Tµmµ

Tµmµ =

N��

s=1

2 [�(Dµ⇤s)�Dµ⇤s + 2U(⇤�s⇤s)] +

N��

f=1

mf ⌅̄f⌅f +�h(g)

2gFµ�Fµ�

Gauge trace anomaly: lowest order decay channel to photonstwo-photon decay of the Higgs

Summery of decay rates

Femions

Scalars

Gauge fields

Probably most efficient.

�(⇥ � ⇤+⇤�) � N⇥[F1(v)]2m3�

64�M4Pl

�(⇥ � ⇤̄⇤) �N⇥[F1(v)]2m�m2

⇥

32�M4Pl

�(⇤ � 2Aµ) =�2[F1(v)]2m3

�

1024⇥3M4Pl

������

N��

f=1

2If

�m2

�

m2f

�+

N��

s=1

�2 +

m2�

m2s

�Is

�m2

�

m2s

�������

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, ...