Non-Gaussianity as a signature of thermal initial condition of inflation

Abstract

We study non-Gaussianities in the primordial perturbations in single field inflation where there is radiation era prior to inflation. Inflation takes place when the energy density of radiation drops below the value of the potential of a coherent scalar field. We compute the thermal average of the two, three and four point correlation functions of inflaton fluctuations. The three point function is proportional to the slow roll parameters and there is an amplification in $f_{NL}$ by a factor of 65 to 90 due to the contribution of the thermal bath, and we conclude that the bispectrum is in the range of detectability with the 21-cm anisotropy measurements. The four point function on the other hand appears in this case due to the thermal averaging and the fact that thermal averaging of four-point correlation is not the same as the square of the thermal averaging of the two-point function. Due to this fact $\tau_{NL}$ is not proportional to the slow-roll parameters and can be as large as -42. The non-Gaussianities in the four point correlation of the order 10 can also be detected by 21-cm background observations. We conclude that a signature of thermal inflatons is a large trispectrum non-Gaussianity compared to the bispectrum non-Gaussianity.Comment: 17 RevTeX4 pages, 2 figures, One paragraph added in Introduction, No further changes made, Accepted for publication in PR

Scale-dependent power spectrum from initial excited-de Sitter modes

“…We will show that this deviation from BD mode can modify power spectrum and in particular can produce scale-dependent power spectrum fit with recent observations. Non-trivial initial states have been studied by many authors, including α-vacuum [20], general multi-mode squeezed states [23][24][25][26][27][28], particle number eigen-states [29], Gaussian and non-Gaussian initial states [30], coherent states and α-states [31,32], thermal states [33], homogeneous initial states [34] and calm states [35]. It is also well known that the inflation can be described in approximate dS space-time [7,36], thus the study of dS and quantum theory of fields in this background is well motivated.…”

Non-Gaussianity consistency relations, initial states and back-reaction

“…For slow-roll inflation it is well known that all the consistency relations are obeyed for the Bunch-Davies initial state [9]. There has been a great deal of work focused on departure from the Bunch-Davies state [15,[25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. In this paper, we will introduce general initial states of both scalar and tensor perturbations built over the Bunch-Davies state and consequently compute the two-point and three-point functions of scalar and tensor perturbations for slow-roll inflation.…”

Primordial non-Gaussianities in single field inflationary models with non-trivial initial states

“…Non-Gaussianities arising from specific classes of nontrivial initial states have been studied by many authors, including particle number eigenstates [25], Gaussian states [26], general multimode squeezed (i.e. vacuum) states [27][28][29][30][31][32][33][34][35], coherent states [36], thermal states [37], and so-called "calm states" [38]. In this paper we shall generalize these results to arbitrary initial states that are homogeneous.…”