  In the presence of self-interactions, the post-inflationary evolution of the
inflaton field is driven into the non-linear regime by the resonant growth of
its fluctuations. The once spatially homogeneous coherent inflaton is converted
into a collection of inflaton particles with non-vanishing momentum.
Fragmentation significantly alters the energy transfer rate to the inflaton's
offspring during the reheating epoch. In this work we introduce a formalism to
quantify the effect of fragmentation on particle production rates, and
determine the evolution of the inflaton and radiation energy densities,
including the corresponding reheating temperatures. For an inflaton potential
with a quartic minimum, we find that the efficiency of reheating is drastically
diminished after backreaction, yet it can lead to temperatures above the big
bang nucleosynthesis limit for sufficiently large couplings. In addition, we
use a lattice simulation to estimate the spectrum of induced gravitational
waves, sourced by the scalar inhomogeneities, and discuss detectability
prospects. We find that a Boltzmann approach allows to accurately predict some
of the main features of this spectrum.
