Scale Invariant Power Spectrum of Inflation using Expanding BEC: Co-ordinate Dependence of Expanding State

Abstract

In [1], it has been shown that for an expanding BEC model with constant background density, the scale invariance of the inflationary power spectrum breaks down when strong dipole-dipole interactions are involved. So, with the aim of studying the scale invariance of the power spectrum, in this work, a Gaussian background density is introduced into the expanding BEC model and the dipole-dipole interaction term is ignored. Within such a setting, it is found that the scale invariance of the inflationary power spectrum is retained in the long wavelength limit. Continuing further, the terms ignored in the long wavelength limit are treated perturbativately using the approach of multiple scale analysis. It is shown that the resulting inflationary power spectrum due to first order amplitude corrections still remains scale invariant.