An asymptotic method for selection of inflationary modes

Abstract

We present some features of early universe cosmology in terms of Hankel functions index ( ν ). Actually, the recent data from observational cosmology indicate that our universe was nearly de Sitter space-time in the early times which results in an approximate scale-invariant spectrum. This imposes some constrains on index ν [1]. These constrains stimulate us to use general solution of inflaton field equation for ν = 3 2 . To obtain the general solution for the inflationary background, we use asymptotic expansion of Hankel functions up to non-linear order of 1 kη . We consider the non-linear modes as the fundamental modes for early universe during the inflation. In this paper, we obtain the general form of the inflationary modes, scale factor expansion, equation of state and some non-linear corrections of power spectrum in terms of index ν . These results are general and in the quasi-de Sitter and de Sitter limit confirm the conventional results.Pacs: 04.62.+v, 98.80.Cq

Large angular scale CMB anisotropy from an excited initial mode

“…Bunch-Davies) limit. In fact, taking into account the resent observational constraint together with the result obtained in [36] motivates us to use quasi-de Sitter curved space-time and excited mode functions. We have seen that slight deviation of the Bunch-Davies mode leads to corrections in the primordial gravitational potential spectra and in the large angular scales CMB anisotropy.…”

“…In addition, as a result of using this excited initial state, it has been shown that we can have particle creation [35]. They have also been used to calculate the scale-dependency of the primordial power spectrum [36]. In this work, it is expected that employing an initial excited de Sitter mode for calculating the primordial perturbed gravitational potential leads to the breaking of angular-scale symmetry in the CMBA power spectrum.…”

“…These motivate us to choose, from among the various possibilities for initial vacuum states of quantum fluctuations, an excited state which is constructed based on an excited de Sitter mode and which leads to the higher order trans-Planckian corrections [32]. Actually, these higher order corrections are produced because the applied non-trivial mode are non-linear (up to second order) with respect to 1 kη [32][33][34]. On the other hand the free parameter with mass dimension as a cutoff scale in the corrections emphasises that the effect of these excited modes is bounded.…”

Higher order corrections to asymptotic-de Sitter inflation

“…If we suppose that cosmic inflation is described by dS space-time, there exists a concrete set of vacuum states invariant under the dS group. However, as we know, an inflationary universe is described by quasi-dS space-time, that may be exact dS in the first approximation [37]. Recently, as an approximate solution for quasi-dS space-time, we have added a perturbative second order term 1 2 ( ±i kτ ) 2 to the dS mode function (18) in [38] and have derived non-linear trans-Planckian corrections in the spectra.…”

A Covariant Approach for Particle Creation in Non-flat Background

“…quasi-de Sitter vacuum. Therefore, we have introduced the asymptotic-de Sitter modes for the first time in [16][17][18][19], as the main vacuum modes during inflation to study the subject of the particle creation. Compared to pure de Sitter inflation, particles created during quasi-de Sitter inflation have effective mass and non-minimal coupling with gravity that appears to be due to the change in the curvature of the space-time from de Sitter one [20,21].…”