Gravitational Modulated Reheating in R2 inflation Jun’ichi Yokoyama with Yuki Watanabe, Physical Review D87(2013)103524 arXiv:1303.5191

What is THE model of inflation that made our Universe? We wish to single out the right model using as many observables as possible.

Observational constraints on inflation as of 2/2013 9 year WMAP results

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

R2 inflation The theory has an extra scalar (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

Only conformally NON-invariant particles are created. 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] -

[Dvali, Gruzinov, Zaldariaga 04, Kofman 03] 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 Spatially constant decay width Spatially modulated decay width Quantum fluctuations of the Higgs condensation make reheating spatially modulated? Any observational trace? ? [Dvali, Gruzinov, Zaldariaga 04, Kofman 03]

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

The story is totally different in Supergravity. 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] scalar curvature superfield chiral superspace density Ricci scalar gravitino B : auxiliary field Ignoring fermions, Ignoring a pseudo-scalar partner of the scalaron, Lagrangian Constraint

Choice of Ketov & Starobinsky Lagrangian Constraint For the original R2 inflation is recovered. The Lagrangian has the same shape but the scalaron mass is different and much larger than that during inflation.

Hubble parameter at the end of inflation Scalaron decay rate through scalar kinetic term Efficient reheating with is possible if fraction of curvature perturbation generated by R2 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. HuHd, LHu, ... denoted by φ 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 During inflation generically acquires a large expectation value and quantum fluctuation . Decay rate of the scalaron is spatially modulated.

Gravitational Modulated Reheating [Suyama & Yamaguchi 2008] values at the end of inflation The spectral index from modulated reheating: Non-Gaussianity from modulated reheating: 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……

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

R2 inflation is still fully consistent with observations and nothing more than that. Still, our model is interesting in its own light since it realizes modulated reheating without introducing any interactions 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.

Conclusion 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.

: scalaron mass