  In the framework of MSSM inflation, matter and gravitino production are here
investigated through the decay of the fields which are coupled to the udd
inflaton, a gauge invariant combination of squarks. After the end of inflation,
the flat direction oscillates about the minimum of its potential, losing at
each oscillation about 56% of its energy into bursts of gauge/gaugino and
scalar quanta when crossing the origin. These particles then acquire a large
inflaton VEV-induced mass and decay perturbatively into the MSSM quanta and
gravitinos, transferring the inflaton energy very efficiently via instant
preheating. Regarding thermalization, we show that the MSSM degrees of freedom
thermalize very quickly, yet not immediately by virtue of the large vacuum
expectation value of the inflaton, which breaks the $SU(3)_C\times U(1)_Y$
symmetry into a residual $U(1)$. The energy transfer to the MSSM quanta is very
efficient, since full thermalization is achieved after only $\mathcal{O}(40)$
complete oscillations. The udd inflaton thus provides an extremely efficient
reheating of the Universe, with a temperature
$T_{reh}=\mathcal{O}(10^8\mathrm{GeV})$ that allows for instance several
mechanisms of baryogenesis. We also compute the gravitino number density from
the perturbative decay of the flat direction and of the SUSY multiplet. We find
that the gravitinos are produced in negligible amount and satisfy cosmological
bounds such as the Big Bang Nucleosynthesis (BBN) and Dark Matter (DM)
constraints.
