Rigidity of cosmic acceleration in a class of k-essence cosmologies

TL;DR

This paper investigates the stability of cosmic acceleration in a broad class of k-essence cosmologies, demonstrating that inflationary and super-inflationary attractors are structurally stable under potential shape variations.

Contribution

It extends previous tachyon cosmology stability results to generalized k-essence models, including phantom and non-phantom cases, establishing the rigidity of inflationary attractors.

Findings

Inflationary and super-inflationary attractors are rigid against potential shape changes.

The study confirms the stability of these attractors in both phantom and non-phantom scenarios.

Structural stability holds as long as conditions for inflation or super-inflation are satisfied.

Abstract

We study the structural stability of a cosmic acceleration (inflation) in a class of k-essence cosmologies against changes in the shape of the potential. Those models may be viewed as generalized tachyon cosmologies and this analysis extends previous results on the structural stability of cosmic acceleration in tachyon cosmologies. The study considers both phantom and non-phantom cases. The concepts of rigidity and fragility are defined through a condition on the functional form of the Hubble factor. Given the known result of the existence of inflationary (non-phantom) and super-inflationary (phantom) attractors we formulate the question of their structural stability. We find that those attractors are rigid in the sense that they never change as long as the conditions for inflation or super-inflation are met.