Cosmological volume acceleration in dust epoch: using scaling solutions and variable cosmological term $\Lambda(t)$ within an anisotropic cosmological model

TL;DR

This paper explores an anisotropic cosmological model with a variable cosmological term, demonstrating accelerated volume expansion during the dust epoch through exact solutions and scaling solutions, aligning with observations of the universe's anisotropy.

Contribution

It introduces an anisotropic extension of scaling solutions with a variable cosmological term, providing exact solutions that describe accelerated expansion in a dust epoch.

Findings

The model achieves accelerated volume expansion compatible with late-time universe observations.

Exact solutions are derived for anisotropic cosmologies with a scalar field and variable $\Lambda(t)$.

The model transitions to a flat FRW cosmology at late times.

Abstract

Under the premise that the current observations of the cosmic microwave background radiation set a very stringent limit to the anisotropy of the universe, we consider an anistropic model in the presence of a barotropic perfect fluid and a homogeneous scalar field, which transits to a flat FRW cosmology for late times in a dust epoch, presenting an accelerated volume expansion. Furtheremore, the scalar field is identified with a varying cosmological term via $V(\phi(t))=2\Lambda(t)$. Exact solutions to the EKG system are obtained by proposing an anisotropic extension of the scaling solutions scenario: $\rm\rho\sim \eta^{-n},\ \rho_\phi\sim \eta^{-m}$, with $\rm\eta^3=a_1a_2a_3$ the volume function of the anistropic model ($\rm a_1,\, a_2,\, a_3$ being the scale factors).