Cosmological solutions from 5D $N=4$ matter-coupled supergravity

From five-dimensional $N=4$ matter-coupled gauged supergravity, smooth time-dependent cosmological solutions, connecting a $dS_{5-d}\times H^d$ (with $d=2,3$) spacetime at early times to a $dS_5$ spacetime at late times, are presented. The solutions are derived from the second-order equations of motion arising from all the gauged theories that can admit $dS_5$ solutions. There are eight such theories constructed from gauge groups of the form $SO(1,1)\times G_{nc}$ and $SO(1,1)^{(n)}_\text{diag}\times G_{nc}$, with $n=2,3$, where $G_{nc}$ is a non-compact gauge factor whose compact part must be embedded entirely in the matter symmetry group of 5D matter-coupled supergravity. Furthermore, we analyze how the cosmological solutions and their corresponding $dS_5$ vacua cannot arise from the first-order equations that solve the second-order field equations.