### [1002.3039] Collapse of Small-Scale Density Perturbations d

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**February 25 2010**At the end of simple single-field 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 matter-dominated phase before the start of the hot big bang. One might therefore expect that density perturbations grow \propto 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 non-linear, 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?

The interesting thing is that if the matter period is long enough a significant range of wavenumbers can become non-linear, 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?