Non-linear Evolution Of Cosmological Perturbations Research Articles

Constraining $ \mathcal{N} $ = 1 supergravity inflation with non-minimal Kähler operators using δN 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, $0.05\leq A_{CMB}\leq 0.09$.

δNformalism

Precise understanding of nonlinear evolution of cosmological perturbations during inflation is necessary for the correct interpretation of measurements of non-Gaussian correlations in the cosmic microwave background and the large-scale structure of the Universe. The ``$\ensuremath{\delta}N$ formalism'' is a popular and powerful technique for computing nonlinear evolution of cosmological perturbations on large scales. In particular, it enables us to compute the curvature perturbation $\ensuremath{\zeta}$ on large scales without actually solving perturbed field equations. However, people often wonder why this is the case. In order for this approach to be valid, the perturbed Hamiltonian constraint and matter-field equations on large scales must, with a suitable choice of coordinates, take on the same forms as the corresponding unperturbed equations. We find that this is possible when (1) the unperturbed metric is given by a homogeneous and isotropic Friedmann-Lema\^{\i}tre-Robertson-Walker metric; and (2) on large scales and with a suitable choice of coordinates, one can ignore the shift vector (${g}_{0i}$) as well as time dependence of tensor perturbations to ${g}_{ij}/{a}^{2}(t)$ of the perturbed metric. While the first condition has to be assumed a priori, the second condition can be met when (3) the anisotropic stress becomes negligible on large scales. However, in order to explicitly show that the second condition follows from the third condition, one has to use gravitational field equations, and thus this statement may depend on the details of the theory of gravitation. Finally, as the $\ensuremath{\delta}N$ formalism uses only the Hamiltonian constraint and matter-field equations, it does not a priori respect the momentum constraint. We show that the error in the momentum constraint only yields a decaying mode solution for $\ensuremath{\zeta}$, and the error vanishes when the slow-roll conditions are satisfied.

Cosmic microwave background bispectrum on small angular scales

This article investigates the nonlinear evolution of cosmological perturbations on sub-Hubble scales in order to evaluate the unavoidable deviations from Gaussianity that arise from the nonlinear dynamics. It shows that the dominant contribution to modes coupling in the cosmic microwave background temperature anisotropies on small angular scales is driven by the sub-Hubble nonlinear evolution of the dark matter component. The perturbation equations, involving, in particular, the first moments of the Boltzmann equation for photons, are integrated up to second order in perturbations. An analytical analysis of the solutions gives a physical understanding of the result as well as an estimation of its order of magnitude. This allows one to quantify the expected deviation from Gaussianity of the cosmic microwave background temperature anisotropy and, in particular, to compute its bispectrum on small angular scales. Restricting to equilateral configurations, we show that the nonlinear evolution accounts for a contribution that would be equivalent to a constant primordial non-Gaussianity of order ${f}_{\mathrm{NL}}\ensuremath{\sim}25$ on scales ranging approximately from $\ensuremath{\ell}\ensuremath{\sim}1000$ to $\ensuremath{\ell}\ensuremath{\sim}3000$.