Constraining $\mathcal{N}=1$ supergravity inflation with non-minimal Kähler operators using $\delta N$ formalism

Abstract

In this paper I provide a general framework based on $\delta N$ formalism to study the features of unavoidable higher dimensional non-renormalizable Kähler operators for $\mathcal{N}=1$ supergravity (SUGRA) during primordial inflation from the combined constraint on non-Gaussianity, sound speed and CMB dipolar asymmetry as obtained from the recent Planck data. In particular I 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 I 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 for a generic class of sub-Planckian models induced by the Hubble-induced corrections for a minimal supersymmetric D-flat direction where inflation occurs at the point of inflection within the visible sector. Hence by using multi parameter scan I constrain the non-minimal couplings appearing in non-renormalizable Kähler operators within, $\mathcal{O}(1)$, for the speed of sound, $0.02\le c_s\le 1$, and tensor to scalar, $10^{-22}\le r_{\star }\le 0.12$. Finally applying all of these constraints I will fix the lower as well as the upper bound of the non-Gaussian parameters within, $\mathcal{O}(1-5)\le f_{NL}\le 8.5$, $\mathcal{O}(75-150)\le {\tau }_{NL}\le 2800$ and $\mathcal{O}(17.4-34.7)\le g_{NL}\le 648.2$, and CMB dipolar asymmetry parameter within the range, $0.05\le A_{CMB}\le 0.09$.

Comments: 26 pages, 5 figures, Accepted for publication in JHEP