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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.
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