The early Universe may have passed through an extended period of matter-dominated expansion following inflation and prior to the onset of radiation domination. Subhorizon density perturbations grow gravitationally during such an epoch, collapsing into bound structures if it lasts long enough. The strong analogy between this phase and structure formation in the present-day Universe allows the use of $N$-body simulations and approximate methods for halo formation to model the fragmentation of the inflaton condensate into inflaton halos. For a simple model we find that these halos have masses of up to 20 kg and radii of the order of ${10}^{-20}\mathrm{m}$, roughly ${10}^{-24}$ seconds after the big bang. We find that the $N$-body halo mass function matches predictions of the mass-peak patch method and the Press-Schechter formalism within the expected range of scales. A long matter-dominated phase would imply that reheating and thermalization occurs in a universe with large variations in density, potentially modifying the dynamics of this process. In addition, large overdensities can source gravitational waves and may lead to the formation of primordial black holes.

• Received 2 December 2020
• Accepted 24 February 2021

DOI:https://doi.org/10.1103/PhysRevD.103.063525