Gravitational Modulated Reheating Jun’ichi Yokoyama with Yuki Watanabe, Physical Review D87(2013) arXiv: Research Center for the Early Universe (RESCEU) Kavli IPMU

Observational constraints on inflation as of 2/ year WMAP results

R 2 inflation is in good shape! Can we further confirm or falsify it with Planck?

R 2 inflation (Starobinsky 1980) The theory has an extra scalar degree of freedom called the “scalaron” with mass M. effective potential inflation reheating M from the amplitude of fluctuations

R 2 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] -

Spatially modulated decay width Spatially constant decay 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] [Kunimitsu and JY 12]

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 constant decay width Spatially modulated decay width By the time the reheating occurs, these terms become negligibly small.

 In an earlier attempt of model building of SUGRA R 2 inflation by Ketov and Starobinsky, 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.

R 2 Inflation in SUGRA [Ketov 2010; Ketov & Starobinsky 2011; Ketov & Tsujikawa 2012] chiral superspace density Ricci scalar scalar curvature superfield Ignoring fermions, Ignoring a pseudo-scalar partner of the scalaron, gravitino B : auxiliary field Lagrangian Constraint and a vector field (which actually causes problems) [Ferrara et al 2013]

Lagrangian Constraint For the original R 2 inflation is recovered. The Lagrangian has the same shape but the scalaron mass is different and much larger than that during inflation. Choice of Ketov & Starobinsky (to be regarded as a toy model now)

Lagrangian Constraint For the original R 2 inflation is recovered. The Lagrangian has the same shape but the scalaron mass is different and much larger than that during inflation. The theory is defined in superspace including two mass scales. Gravity in this theory is described by The Lagrangian during inflation

Lagrangian Constraint For the original R 2 inflation is recovered. The Lagrangian has the same shape but the scalaron mass is different and much larger than that during inflation. The theory is defined in superspace including two mass scales. Gravity in this theory is described by The Lagrangian during reheating

Hubble parameter at the end of inflation Scalaron decay rate through scalar kinetic term Efficient reheating with is possible if The parameter λ represents the fraction of curvature perturbation generated by R 2 inflation Number of e-folds of the pivot scale We take hereafter, so that the Universe is reheated immediately after inflation.

In SUSY, there are a number of flat directions in the scalar potential which has much flatter than the potential of the standard Higgs field. H u H d, LH u,... denoted by φ During inflation generically acquires a large expectation value and quantum fluctuation. 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: m 0 ~ 1 TeV << H, M X = cutoff scale

Gravitational Modulated Reheating The spectral index from modulated reheating: Non-Gaussianity from modulated reheating: [Suyama & Yamaguchi 2008] values at the end of inflation is the value of the flat direction when the pivot scale left the Hubble radius, which is treated as a parameter satisfying.

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, and submitted our paper to the arXiv 5 min. before the Planck press conference……

and the Result was… Planck+WMAP pol.+lensing: or Our model Our model was neither falsified nor confirmed.

R 2 inflation is still fully consistent with observations and nothing more than that. Still, gravitational modulated reheating scenario is interesting in its own light since it realizes modulated reheating without introducing any interactions by hand.

Inflation models whose reheating proceeds through gravitational particle production such as the R 2 inflation may be associated with modulated reheating since the mass terms, which breaks the conformal invariance and relevant to particle production, are spatially fluctuating due to the quantum fluctuations acquired by SUSY flat direction. Ketov-Starobinsky type SUGRA R 2 inflation + modulated reheating scenario is consistent with Planck 2013 results. But this model should be further worked out since it neglects vector fields which actually makes the auxiliary field X propagate. Conclusion

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 n s, which favors larger λ, does not yield any sizable f NL. The higher allowed value like n s =0.967 yields From the formula of n s, the smaller N allows smaller λ resulting in higher values of |f NL |. Thermal inflation scenario may yield such values.

: scalaron mass