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.
