Towards a de Sitter quintom-like cosmology from a reduction of a 7-dimensional $BF$ theory

Abstract

In this article, we analyze a 7-dimensional $BF$ theory that, upon dimensional reduction, transforms into an effective 4-dimensional action in which a generic metric is involved. A constraint is imposed in such a way that this is the Friedmann-Lema\^{i}tre-Robertson-Walker metric characterized by a scale factor $a(t)=\mathrm{exp}(H_0 t)$ with a Hubble constant $H_{0}=67.70 \,\rm [km\, s^{-1}\,Mpc^{-1}]$. We also compute the barotropic parameter $\omega \equiv p/\rho$ from our solutions. Three different scenarios are explored, in which the model transitions from quintessence to phantom regimes, crossing the theoretical phantom divide line. Consequently, the effective action represents a quintom-like scenario. Moreover, we derive some analytic solutions for the scale factor by treating it as a dynamical variable in the effective action. In this case, different outcomes are obtained, where the model can transit from a cosmological constant to a quintessence regime; however, it cannot cross the theoretical phantom divide line. However, this simplistic model successfully captures distinct phases of cosmic expansion.