Abstract
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, $0.05\leq A_{CMB}\leq 0.09$.
Highlights
Has shifted towards the study of nonlinear evolution of cosmological perturbations
In this paper I will concentrate our study for Hubble induced inflection point MSSM inflation derived from various higher dimensional Planck scale suppressed non-minimal Kahler operators in N = 1 supergravity (SUGRA) which satisfies the observable universe, and it is well motivated for providing an example of visible sector inflation
0.02 < cs < 1). 8The upper bound of the CMB dipolar asymmetry parameter (ACMB) can be expressed in terms of the non-Gaussian parameter fNloLcal through a consistency relation as [57], ACMB 10−1fNloLcal, which perfectly holds good in the present effective theory setup
Summary
The inflaton superfield Φ is made up of D-flat direction within MSSM and they are usually lifted by the F -term [31] of the non-renormalizable operators as appearing in the superpotential. Where for MSSM D-flat directions, n ≥ 3 (In the present context n characterizes the dimension of the non-renormalizable operator) and the coupling, λ ∼ O(1). We concentrate on two MSSM flat directions, LLe and udd, which can drive inflation with n = 6 via R-parity invariant (LLe)(LLe)/Mp3 and (udd)(udd)/Mp3 operators in the visible sector, which are lifted by themselves [32,33,34], where u, d denote the right handed squarks, and L denotes that left handed sleptons and e denotes the right handed slepton
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