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

In this paper I provide a general framework based on $δN$ formalism to study the features of unavoidable higher dimensional non-renormalizable Kähler operators for ${\cal N}=1$ 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, $ζ$, without solving the exact perturbed field equations. Further I compute the non-Gaussian parameters $f_{NL}$, $τ_{NL}$ and $g_{NL}$ for local type of non-Gaussianities and CMB dipolar asymmetry parameter, $ A_{CMB}$, using the $δN$ 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, ${\cal O}(1)$, for the speed of sound, $0.02\leq c_s\leq 1$, and tensor to scalar, $10^{-22} \leq r_{\star} \leq 0.12$. Finally applying all of these constraints I will fix the lower as well as the upper bound of the non-Gaussian parameters within, ${\cal O}(1-5)\leq f_{NL}\leq 8.5$, ${\cal O}(75-150)\leqτ_{NL}\leq 2800$ and ${\cal O}(17.4-34.7)\leq g_{NL}\leq 648.2$, and CMB dipolar asymmetry parameter within the range, $0.05\leq A_{CMB}\leq 0.09$.