At the end of simple singlefield inflation models the field can oscillate about the minimum where [tex]V\propto m^2\phi^2[/tex] before the universe reheats. The average equation of state is like matter (c.f. 0805.1748), so there is effectively a matterdominated phase before the start of the hot big bang. One might therefore expect that density perturbations grow ∝ a as usual. This paper recovers this result in more detail by explicitly solving for the perturbations in the oscillating background and describes as how the perturbation growth can be interpreted as arising from a preheating instability. It is a nice fairly simple calculation, I'm surprised it has not been done before! (?)
The interesting thing is that if the matter period is long enough a significant range of wavenumbers can become nonlinear, potentially giving primordial black holes (PMBs) and sourcing gravitational waves as discussed in their second paper (1002.3278, and previously in 0901.0989 and other papers). Does all this actually lead to an interesting constraint on the inflation model/reheating temperature?
[1002.3039] Collapse of SmallScale Density Perturbations during Preheating in Single Field Inflation
Authors:  Karsten Jedamzik (LPTA), Martin Lemoine (IAP), Jerome Martin (IAP) 
Abstract:  After cosmic inflation and before the transition to radiation domination, the cosmic energy density may have been dominated during an extended period by an oscillating massive scalar condensate. We show that during this period, subHubble scale perturbations are subject to a metric preheating instability in the narrow resonance regime. We analyze in detail both, quadratic and quartic potentials. The instability leads to the growth of density perturbations which in many cases become nonlinear already before the beginning of a radiation dominated Universe. This is particularly the case when requiring a phenomenologically preferred low reheat temperature. These early structures may lead to the emission of gravitational waves and the production of primordial black holes. Furthermore, it is not clear if they could modify the prediction of linear curvature perturbations on very large scales. 
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