  We study a homogeneously driven granular fluid of hard spheres at
intermediate volume fractions and focus on time-delayed correlation functions
in the stationary state. Inelastic collisions are modeled by incomplete normal
restitution, allowing for efficient simulations with an event-driven algorithm.
The incoherent scattering function, F_incoh(q,t), is seen to follow
time-density superposition with a relaxation time that increases significantly
as volume fraction increases. The statistics of particle displacements is
approximately Gaussian. For the coherent scattering function S(q,omega) we
compare our results to the predictions of generalized fluctuating hydrodynamics
which takes into account that temperature fluctuations decay either diffusively
or with a finite relaxation rate, depending on wave number and inelasticity.
For sufficiently small wave number q we observe sound waves in the coherent
scattering function S(q,omega) and the longitudinal current correlation
function C_l(q,omega). We determine the speed of sound and the transport
coefficients and compare them to the results of kinetic theory.
