Equation of State and Duration to Radiation Domination after Inflation

Abstract

We calculate the equation of state after inflation and provide an upper bound on the duration before radiation domination by taking the nonlinear dynamics of the fragmented inflaton field into account. A broad class of single-field inflationary models with observationally consistent flattening of the potential at a scale M away from the origin, V ( ϕ ) ∝ | ϕ | 2 n near the origin, and where the couplings to other fields are ignored, is included in our analysis. We find that the equation of state parameter w → 0 for n = 1 and w → 1 / 3 (after sufficient time) for n ≳ 1 . We calculate how the number of e -folds to radiation domination depends on both n and M when M ∼ m Pl , whereas when M ≪ m Pl , we find that the duration to radiation domination is negligible. Our results are explained in terms of a linear instability analysis in an expanding universe and scaling arguments, and are supported by 3 + 1 -dimensional lattice simulations. We show that our upper bound on the postinflationary duration before radiation domination reduces the uncertainty in inflationary observables even when couplings to additional light fields are included (at least under the assumption of perturbative decay).