Analytic Approximations for the Primordial Power Spectrum with Israel Junction Conditions

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.