Cosmological solutions from 4D $N=4$ matter-coupled supergravity

TL;DR

This paper constructs smooth, time-dependent cosmological solutions in 4D $N=4$ supergravity that evolve from a $dS_2\times \Sigma_2$ geometry to a $dS_4$ universe, exploring different gauged theories and their solution spaces.

Contribution

It provides explicit cosmological solutions connecting lower-dimensional de Sitter spaces to four-dimensional de Sitter spacetime within $N=4$ supergravity, analyzing solution existence and equations.

Findings

Solutions interpolate between $dS_2\times \Sigma_2$ and $dS_4$

Type I theories admit both $dS$ and $AdS$ solutions

Type II theories admit only $dS$ solutions

Abstract

From four-dimensional $N=4$ matter-coupled gauged supergravity, we study smooth time-dependent cosmological solutions interpolating between a $dS_2\times \Sigma_2$ spacetime, with $\Sigma_2 = S^2$ and $H^2$, in the infinite past and a $dS_4$ spacetime in the infinite future. The solutions were obtained by solving the second-order equations of motion from all the ten gauged theories known to admit $dS_4$ solutions, of which there are two types. Type I $dS$ gauged theories can admit both $dS$ solutions as well as supersymmetric $AdS$ solutions while type II $dS$ gauged theories only admit $dS$ solutions. We also study the extent to which the first-order equations that solve the aforementioned second-order field equations fail to admit the $dS_4$ vacua and their associated cosmological solutions.