  Light massive preheat fields acquire a non-vanishing dispersion during
parametric resonance from their quantum particle production. This in turn will
modify the inflaton potential, which in some cases can induce a transient
period of acceleration. We illustrate this phenomenon in the setup of
non-supersymmetric non-minimal M-flation (non-$\mathbb{M}$-flation) which has
some motivations from the brane compactifications in string theory.
Implementing a lattice simulation by the LATTICEEASY code, we compute the
potential correction term in our scenario and show that the modified term
indeed causes the universe to make a transition from the decelerated expansion
to a temporary phase of acceleration. The correction term reduces to some
extent the number density of the particles generated during preheating, but the
efficiency of preheating remains still enough to have successful particle
production after inflation. We also compute the spectrum of the gravitational
waves (GWs) generated during preheating in our setup by using the LATTICEEASY
code. Although the peak frequency remains almost the same, the inclusion of the
correction term reduces the amplitude of the gravitational spectrum by almost
one order of magnitude.
