  We investigate the large deviation function pi(w) for the fluctuations of the
power W(t)=w t, integrated over a time t, injected by a homogeneous random
driving into a granular gas, in the infinite time limit. Starting from a
generalized Liouville equation we obtain an equation for the generating
function of the cumulants mu(lambda) which appears as a generalization of the
inelastic Boltzmann equation and has a clear physical interpretation.
Reasonable assumptions are used to obtain mu(lambda) in a closed analytical
form. A Legendre transform is sufficient to get the large deviation function
pi(w). Our main result, apart from an estimate of all the cumulants of W(t) at
large times t, is that pi(w) has no negative branch. This immediately results
in the failure of the Gallavotti-Cohen Fluctuation Relation (GCFR), that in
previous studies had been suggested to be valid for injected power in driven
granular gases. We also present numerical results, in order to discuss the
finite time behavior of the fluctuations of W(t). We discover that their
probability density function converges extremely slowly to its asymptotic
scaling form: the third cumulant saturates after a characteristic time larger
than 50 mean free times and the higher order cumulants evolve even slower. The
asymptotic value is in good agreement with our theory. Remarkably, a numerical
check of the GCFR is feasible only at small times, since negative events
disappear at larger times. At such small times this check leads to the
misleading conclusion that GCFR is satisfied for pi(w). We offer an explanation
for this remarkable apparent verification. In the inelastic Maxwell model,
where a better statistics can be achieved, we are able to numerically observe
the failure of GCFR.
