21-26 July 2014

Renold Building

Europe/London timezone

# Constraining N=1 supergravity inflationary framework with non-minimal Kähler operators

Presented by Mr. Sayantan CHOUDHURY
on
21 Jul 2014
from
15:30
to
15:50

## Content

In this work we will illustrate how to constrain unavoidable K\"ahler corrections for N=1 supergravity (SUGRA) inflation from the recent Planck data. We will show that the non-renormalizable K\"ahler operators will induce in general non-minimal kinetic term for the inflaton field, and two types of SUGRA corrections in the potential - the Hubble-induced mass ($c_{H}$), and the Hubble-induced A-term (aH) correction. The entire SUGRA inflationary framework can now be constrained from (i) the speed of sound, $c_{s}$, and (ii) from the upper bound on the tensor to scalar ratio, $r_{*}$. We will illustrate this by considering a heavy scalar degree of freedom at a scale, Ms, and a light inflationary field which is responsible for a slow-roll inflation. We will compute the corrections to the kinetic term and the potential for the light field explicitly. As an example, we will consider a visible sector inflationary model of inflation where inflation occurs at the point of inflection, which can match the density perturbations for the cosmic microwave background radiation, and also explain why the universe is filled with the Standard Model degrees of freedom. We will scan the parameter space of the non-renormalizable K\"ahler operators, which we find them to be order ${\cal O}(1)$, consistent with physical arguments. While the scale of heavy physics is found to be bounded by the tensor-to scalar ratio, and the speed of sound, ${\cal O}(10^{11}\leq M_{s}\leq 10^{16})$ GeV, for $0.02\leq c_{s}\leq 1$ and 10^{−22}\leq r_{*}\leq 0.12$. In particular we study the nonlinear evolution of cosmological perturbations on large scales which enables us to compute the curvature perturbation, $\zeta$, without solving the exact perturbed field equations. Further we compute the non-Gaussian parameters $f_{NL}$ , $\tau_{NL}$ and $g_{NL}$ for local type of non-Gaussianities and CMB dipolar asymmetry parameter, $A_{CMB}$, using the $\delta N$ formalism. Hence by using multi parameter scan we will fix the lower as well as the upper bound of the non-Gaussian parameters within, ${\cal O}(1−5)\leq f_{NL}\leq 8.5$, ${\cal O}(75−150)\leq \tau_{NL}\leq 2800$ and ${\cal O}(17.4−34.7)\leq g_{NL}\leq 648.2$, and CMB dipolar asymmetry parameter within the range, $0.05\leq A_{CMB}\leq 0.09$.

## Summary

In this paper, we have shown that in any ${\cal N}=1$
SUGRA inflation model when ever there are more degrees of freedom, non-minimal K\"ahler corrections would induce three distinct types of corrections: (i) non-minimal kinetic term for the inflaton, (ii) Hubble-induced mass correction to the inflaton, and (iii) Hubble-induced $A$-term in the potential.
The exact nature of K\"ahler potential and K\"ahler corrections might not be known in all possible scenarios, but our aim has been to constrain the coefficients of the non-renormalizable K\"ahler higher dimensional operators phenomenologically, which are gauge invariant,
from the recent Planck data. We assumed minimal K\"ahler potentials for all the fields to begin with. We first considered the heavy physics to be completely decoupled from the dynamics of the light inflaton field. We considered the light field to be embedded within MSSM, such that the reheating of the universe is guaranteed to be that of the SM dof. In the simplest setup when the heavy field is well settled down in its potential, it only affects via its vacuum energy density. The kinetic terms are mostly canonical, and therefore we do not obtain any constraint on the coefficients of the dimensional $3$ and $4$ non-reormalizable K\"ahler operators.
We further investigated an intriguing possibility, when the heavy field is coherently oscillating with a frequency larger than the Hubble parameter during the onset of inflation, while the light field is slowly rolling over the potential. In this particular scenario, we were able to constrain the coefficients of the Planck suppressed K\"ahler operators of dimensional $3$ and $4$. We scanned the non-minimal parameters and obtained a region of the parameter space where we can satisfy the current Planck observations, i.e.
$P_S,~n_S,~c_s$ and $r_\star$ (within $2\sigma$~CL), non-Gaussian parameters: $f_{NL}^{local},\tau_{NL}^{local}$ (within $1\sigma-1.5\sigma$~CL) and CMB dipolar asymmetry parameter $A_{CMB}$ (within $2\sigma$~CL), and we obtained all the coefficients to be of order ${\cal O}(1)$, as naturally expected in any non-renormalizable SUGRA theory.
For the range of parameter space scanned, we were able to set an upper limit on the scale of new physics from the constraints arising from $r_\star$, which we obtained
to be within $10^{11}\leq M_s\leq 10^{16}$~GeV. For the lower bound on $M_s$, we found $r_\star\sim {\cal O}(10^{-22})$ and extremely negligible, and for the upper bound we saturated $r_\star =0.12$.
Using this methodology, I have obtained the theoretical upper and lower bound on the non-Gaussian parameters within the range, ${\cal O}(1-5)\leq f_{NL}\leq8.5$, ${\cal O}(75-150)\leq\tau_{NL}<2800$
and ${\cal O}(17.4-34.7)\leq g_{NL}\leq 648.2$, and the CMB dipolar asymmetry parameter within, $0.05\leq A_{CMB}\leq0.09$
Finally, we would like to mention that all the above bounds have been obtained for a very particular kind of inflation model, which
is fully embedded within MSSM, the inflaton is an MSSM flat direction and inflation happens at the point of inflection with a fine tuned parameter at the inflection point is roughly one partin $10^{4}$. We chose MSSM inflation for its advantage that the dynamics can be well understood during inflation ad after inflation. In particularly, we can ascertain that the Universe after inflation would be filled with the SM degrees of freedom and also the model is capable of explaining the Higgs mass constraint and the dark matter abundance. Not every model of inflation enjoys such advantages, and therefore studying this model in some details along with SUGRA corrections yielded interesting constraints. Our methodology can be followed for other kinds of inflationary models too.
There is also a future prospect of upgrading the present methodology proposed in this paper by studying the further stringent phenomenological constraints on the non-minimal couplings, as appearing in the context of higher dimensional Planck scale suppressed K\"ahler operators within N=1 SUGRA by imposing the constraint on Higgs mass and the dark matter abundance via WIMPy baryogenesis scenario.

## Place

Location: Renold

Room: F14

## Primary authors

- Mr. Sayantan CHOUDHURY Senior Research Fellow, Physics & Applied Mathematics Unit, Indian Statistical Institute,Kolkata,India