Inflation in Non-de Sitter Background with Coherent States

Abstract

We use the excited coherent states built over the initial non-de Sitter modes, to study the modification of spectra of primordial scalar fluctuation. Non-de Sitter modes are actually the asymptotic solution of the inflaton field equation[JHEP 09(2014) 020]. We build excited coherent states over the non-de Sitter modes and despite the lack of interactions in the Lagrangian, we find a non-zero one-point function. It is shown that the primordial non-Gaussianity resulting from excited-de Sitter modes depend both of time and background space-time. It is very tiny of order (≤ 10 −24 ) , at the Planck initial fixed time that confirmed by resent observations for single field inflation but it grows in the present epoch. Moreover, our results at the leading order are similar to what obtained with general initial states and in the dS limit leads to standard results [JCAP 1202[JCAP (2012 005]. We will show that the non-dS modes and its resulting spectrum are more usable for far past time limit.Pacs: 04.62.+v, 04.25.-g, 98.80.Cq Since the Bunch-Davies(BD) mode [34] is used just for pure de Sitter(dS) space-time i.e. ν = 3/2 , this range of ν motivates us to consider non-dS modes for quasi(excited)-dS space-time.

Quasi-de sitter solution, negative norm state and Krein space in cosmology

“…according to the asymptotic expansion (31) and the equation of motion (7), the most general form of mode functions u k for curved space-time becomes as [17,[40][41][42][43]:…”