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

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

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

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

6. 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

7. 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.

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

9. [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]

10. 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.

11. 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.

12. 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

13. 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.

14. 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.

15. 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.

16. 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

17. 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……

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

19. 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.

20. 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.

21. 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.

23. : scalaron mass