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In the framework of MSSM inflation, matter and gravitino production are hereinvestigated through the decay of the fields which are coupled to the uddinflaton, a gauge invariant combination of squarks. After the end of inflation,the flat direction oscillates about the minimum of its potential, losing ateach oscillation about 56% of its energy into bursts of gauge/gaugino andscalar quanta when crossing the origin. These particles then acquire a largeinflaton VEV-induced mass and decay perturbatively into the MSSM quanta andgravitinos, transferring the inflaton energy very efficiently via instantpreheating. Regarding thermalization, we show that the MSSM degrees of freedomthermalize very quickly, yet not immediately by virtue of the large vacuumexpectation 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 veryefficient, since full thermalization is achieved after only $\mathcal{O}(40)$complete oscillations. The udd inflaton thus provides an extremely efficientreheating of the Universe, with a temperature$T_{reh}=\mathcal{O}(10^8\mathrm{GeV})$ that allows for instance severalmechanisms of baryogenesis. We also compute the gravitino number density fromthe perturbative decay of the flat direction and of the SUSY multiplet. We findthat the gravitinos are produced in negligible amount and satisfy cosmologicalbounds such as the Big Bang Nucleosynthesis (BBN) and Dark Matter (DM)constraints.

Reheating, thermalization and non-thermal gravitino production in MSSM inflation