Constraining ${\cal N}=1$ supergravity inflation with non-minimal
  K\"ahler operators using $\delta N$ formalism
  In this paper I provide a general framework based on $\delta N$ formalism to
study the features of unavoidable higher dimensional non-renormalizable
K\"ahler 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, $\zeta$, 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 K\"ahler 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, ${\cal
O}(1-5)\leq f_{NL}\leq 8.5$, ${\cal O}(75-150)\leq\tau_{NL}\leq 2800$ and
${\cal O}(17.4-34.7)\leq g_{NL}\leq 648.2$, and CMB dipolar asymmetry parameter
within the range, $0.05\leq A_{CMB}\leq 0.09$.
