Gravitational Modulated Reheating in R2 inflation

Jun’ichi Yokoyama

with Yuki Watanabe, Physical Review D87(2013)103524

arXiv:1303.5191

Observational constraints on inflation as of 2/20139 year WMAP results

R2 inflation is in good shape!Can we further confirm or falsify it with Planck?

snrNLf( )P k

RT

s

Tn

24 4

2 2 2

1 1( )

2 6 2

RS R gd x f R gd x

M

R2 inflation (Starobinsky 1980)

The theory has an extra scalardegree of freedom called the“scalaron” with mass M.

effective potential

inflation

reheating

M

p PlM M

1PlM

from the amplitude of fluctuations

R2 inflation is followed by oscillation of the Hubble parameter, which reheats the Universe through gravitational particle production.

Only conformally NON-invariant particles are created.

In the scalaron picture, this can be understood by the decay of the oscillating scalaron field.

two body decay to scalar particles σ and fermions ψ.

σ : is created even if it is massless, because its kinetic term is not conformally invariant.

ψ : is created only if its mass term is nonvanishing so that conformal invariance is broken.

Reheating by scalaron decay [Watanabe & Komatsu 2007; Faulkner et al 2007; Gorbunov & Panin 2011]

-

m

Spatially modulateddecay width

Spatially constantdecay width

Quantum fluctuations of the Higgs condensation make reheating spatially modulated? Any observational trace?

Masses of σ and ψ are given by VEV of the Higgs field which may acquire a large value during inflation due to quantum fluctuations = Higgs Condensation

Higgs field

? [Dvali, Gruzinov, Zaldariaga 04, Kofman 03]

, , Higgs Higgs Higgs Higgs Higgsm h m y

Higgs

However, since the scalaron mass is so small that it does not decay until long after inflation. In the oscillation regime, the Higgs field also oscillates with a quartic potential and decreases its amplitude.

Spatially constantdecay width

Spatially modulateddecay width

By the time the reheating occurs,these terms become negligibly small.

In SUGRA R2 inflation, the scalaron mass in the reheating regime is much larger than that during inflation, so that efficient reheating is possible.

In Supersymmetric theories there exist a number of flat directions in the scalar potential, which has much flatter potential than the standard Higgs field, so that they may acquire a large quantum fluctuations which may affect the gravitational reheating.

R2 Inflation in SUGRA [Ketov 2010; Ketov & Starobinsky 2011; Ketov & Tsujikawa 2012]

( )e x g

:

chiral superspace density Ricci scalar

scalar curvature superfield

Ignoring fermions,

Ignoring a pseudo-scalar partner of the scalaron,

gravitino B : auxiliary field

1PlM

( , )X X F F

Lagrangian

Constraint

Choice of Ketov & Starobinsky

Lagrangian

Constraint221

10

M

For the original R2 inflationis recovered.m M

The Lagrangian has the same shapebut the scalaron mass is differentand much larger than that duringinflation.

m

Hubble parameter at the end of inflation

Scalaron decay rate through scalar kinetic term

fH Efficient reheating with is possible if

fraction of curvature perturbation generated by R2 inflation

Number of e-folds ofthe pivot scale

We take hereafter, so that the Universe is reheated immediately after inflation.

rhm m

In SUSY, there are a number of flat directions inthe scalar potential which has much flatter than the potential of the standard Higgs field.

HuHd, LHu, ... denoted by φ

During inflation generically acquires a large expectation valueand quantum fluctuation .

m m m

Decay rate of the scalaron is spatially modulated.

A generic flat direction φ acquires a potential only through SUSY breaking and possible non-renorm. terms in the superpotential:

m0 ~ 1 TeV << H, MX = cutoff scale

( : scalaron)

Gravitational Modulated Reheating

The spectral index from modulated reheating:

Non-Gaussianity from modulated reheating:

[Suyama & Yamaguchi 2008]

values at the end of inflation

1 (2 4)(1 ) nf

is the value of the flat direction when the pivot scale left the Hubble radius, which is treated as a parameter satisfying .2( ) fV H

Modulated reheating through SUSY flat directions The spectral index of total ζ:

The full non-Gaussianity:

Min. K at Δ=0 and max. K at Δ=0.682 for n=4 and Δ=0.451 for n=6.

We find the local non-Gaussianity in the range

7.9 13.5localNLf , and submitted our paper to the

arXiv 5 min. before the Planck press conference……

and the Result was… Planck+WMAP pol.+lensing:

2.7 5.8localNLf or 8.9 14.3 (95%)local

NLf

7.9 13.5localNLf Our model

Our model was neither falsified nor confirmed.

R2 inflation is still fully consistent with observationsand nothing more than that.Still, our model is interesting in its own light since it realizes modulated reheating without introducing anyinteractions by hand.

More comparison with Planck 2013 Planck+WMAP pol.+lensing:

These results are basically in good agreement with the predictions of our model.The lower value of ns, which favors larger λ, does not yield any sizable fNL.

The higher allowed value like ns=0.967 yields

From the formula of ns, the smaller N allows smaller λ resulting in higher values of |fNL|. Thermal inflation scenario may yield such values.

• We have reconsidered cosmic history after R2 inflation in SUGRA in which reheating proceeds through gravitational particle production of conformally non-invariant fields.

• Conformal invariance is broken through a nonvanishing expectation value of a SUSY flat direction whose fluctuations induce modulated reheating.

• SUGRA R2 inflation + modulated reheating scenario is consistent with Planck 2013 results.

Conclusion

sM : scalaron mass