Cosmological singularities and analytical solutions in varying vacuum cosmologies

TL;DR

This paper explores the dynamics of varying vacuum cosmologies with polynomial $b4$ in the Hubble parameter, providing new analytical solutions and analyzing stability of key cosmological eras.

Contribution

It introduces new analytical solutions for $b4(H)$ cosmologies and analyzes their stability, linking specific models to Milne and $R_h=ct$ universes.

Findings

Identified classes of $b4(H)$ models with analytical solutions.

Determined stability of solutions corresponding to different cosmological eras.

Found Milne and $R_h=ct$ models as perturbations, with the latter being unstable.

Abstract

We investigate the dynamical features of a large family of running vacuum cosmologies for which $\Lambda$ evolves as a polynomial in the Hubble parameter. Specifically, using the critical point analysis we study the existence and the stability of singular solutions which describe de-Sitter, radiation and matter dominated eras. We find several classes of $\Lambda(H)$ cosmologies for which new analytical solutions are given in terms of Laurent expansions. Finally, we show that the Milne universe and the $R_{h}=ct$ model can be seen as perturbations around a specific $\Lambda(H)$ model, but this model is unstable.