Reconstruction methods and the amplification of the inflationary spectrum

TL;DR

This paper investigates how different inflationary evolution scenarios affect the scalar perturbation spectrum, highlighting conditions that lead to spectrum amplification or blue tilt, with implications for inflation models.

Contribution

It provides a detailed analysis of the impact of transient inflationary phases on the scalar spectrum, including general relativity and induced gravity frameworks.

Findings

Certain inflationary evolutions cause spectrum amplification.

Presence of a growing Mukhanov-Sasaki solution leads to spectrum enhancement.

Specific inflation models exhibit blue-tilted spectra under certain conditions.

Abstract

We analyze the consequences of different evolutions of the Hubble parameter on the spectrum of scalar inflationary perturbations. The analysis is restricted to inflationary phases described by a transient evolution, when uncommon features arise in the inflationary spectra that may lead to an amplitude enhancement. We then discuss how the spectrum is, respectively, amplified or blue-tilted in the presence or absence of a growing solution of the Mukhanov-Sasaki equation. The cases of general relativity with a minimally coupled inflaton and that of induced gravity are considered explicitly. Finally, some remarks on constant roll inflation are discussed.