Analytic Approximations for the Primordial Power Spectrum with Israel Junction Conditions

TL;DR

This paper compares different matching conditions for primordial perturbations, finds inconsistencies with some assumptions, and proposes an alternative semi-analytic model for more realistic primordial power spectra during finite cosmological phase transitions.

Contribution

It identifies inconsistencies in common matching assumptions and introduces a semi-analytic approach for modeling primordial spectra during phase transitions.

Findings

Contaldi et al.'s matching conditions are inconsistent with Israel junction conditions.

Physically motivated matching leads to unrealistic primordial spectra.

Proposes a semi-analytic model for finite-duration phase transitions.

Abstract

This work compares cosmological matching conditions used in approximating generic pre-inflationary phases of the universe. We show that the joining conditions for primordial scalar perturbations assumed by Contaldi et al. are inconsistent with the physically motivated Israel junction conditions, however; performing general relativistic matching with the aforementioned constraints results in unrealistic primordial power spectra. Eliminating the need for ambiguous matching, we look at an alternative semi-analytic model for producing the primordial power spectrum allowing for finite duration cosmological phase transitions.