In the model of MSSM inflation, the inflaton is a D-flat direction in
the scalar potential, consisting of the supersymmetric partners of
quarks and leptons. Since its couplings to matter are known via the
Minimal Supersymmetric Standard Model (MSSM) interactions, it is
possible to study the particle production at the end of inflation in
great detail, and to track the thermal history of the universe
accordingly. This is a striking difference with respect to inflationary
models where the inflaton is an arbitrary gauge singlet. In this talk
(which is based on arXiv:1103.2123 [hep-ph]), I will
address the production of matter and thermalization via the decay of
the LLe inflaton, namely of a gauge invariant combination of sleptons.
After the end of inflation, the inflaton oscillates coherently about the
minimum of its potential, producing gauge/gaugino and (s)lepton
quanta, which then decay very quickly to (s)quarks. After about 100
oscillations - albeit within one Hubble time - the amplitude of inflaton
oscillations becomes sufficiently small, and all of the degrees of
freedom will thermalize. This provides by far the most efficient reheating of the universe with
the observed degrees of freedom.