  The importance of roughness in the modeling of granular gases has been
increasingly considered in recent years. In this paper, a freely evolving
homogeneous granular gas of inelastic and rough hard disks or spheres is
studied under the assumptions of the Boltzmann kinetic equation. The
homogeneous base state reached by the system is studied from a theoretical
point of view using a Sonine approximation, in contrast to a previous
Maxwellian approach. A general theoretical description is done in terms of
$d_t$ translational and $d_r$ rotational degrees of freedom, which accounts for
the cases of spheres ($d_t=d_r=3$) and disks ($d_t=2$, $d_r=1$) within a
unified framework. The non-Gaussianities of the velocity distribution function
of this state are determined by means of the first nontrivial cumulants and by
the derivation of non-Maxwellian high-velocity tails. The results are validated
by computer simulations using direct simulation Monte Carlo and event-driven
molecular dynamics algorithms.
