Breaking scale invariance from a singular inflaton potential

Abstract

In this paper we break the scale invariance of the primordial power spectrum of curvature perturbations of inflation. Introducing a singular behaviour due to spontaneous symmetry breaking in the inflaton potential, we obtain fully analytic expressions of scale dependent oscillation and a modulation in power on small scale in the primordial spectrum. And we give the associated cosmic microwave background and matter power spectra which we can observe now and discuss the signature of the scale dependence. We also address the possibility of whether some inflationary model with featured potential might mimic the predictions of the scale invariant power spectrum. We present some examples which illustrate such degeneracies.