Slow-roll inflationary senario in the maximally extended background

TL;DR

This paper explores slow-roll inflation within a positively curved universe, deriving power spectra and analyzing how curvature influences observable parameters like the tensor-scalar ratio, aligning with current observational data.

Contribution

It presents a novel analysis of inflationary perturbations in a positively curved FLRW universe, including derivation of power spectra and curvature effects on perturbation amplitudes.

Findings

Curvature spectral index has a small negative running compatible with observations.

Tensor-scalar ratio depends on the perturbation wavelength in curved models.

Curvature influences the relative amplitude of scalar and tensor perturbations.

Abstract

During the inflationary epoch,geometry of the universe may be described by quasi-de Sitter space. On the other hand,maximally extended de Sitter metric in the comoving coordinates accords with a special FLRW model with positive spatial curvature,so in this article we focus on the positively curved inflationary paradigm.For this purpose,first we derive the power spectra of comoving curvature perturbation and primordial gravitational waves in a positively curved FLRW universe according to the slowly rolling inflationary senario. It can be shown that the curvature spectral index in this model automatically has a small negative running parameter which is compatible with observational measurements.Then,by taking into account the curvature factor,we investigate the relative amplitude of the scalar and tensor perturbations.It would be clarified that the tensor-scalar ratio for this model against the spatially flat one,depends on the waelength of the perturbative models directly.