Equation of state during (p)reheating with trilinear interactions

TL;DR

This paper models the universe's post-inflationary evolution with trilinear inflaton interactions, revealing a temporary deviation in the equation of state and its impact on gravitational wave predictions.

Contribution

It provides a detailed simulation of the equation of state during preheating with trilinear interactions, combining lattice and Boltzmann methods for accurate cosmological predictions.

Findings

The equation of state temporarily deviates from zero due to tachyonic resonance.

The inflaton mode eventually dominates, returning the equation of state to zero.

Accounting for the return reduces gravitational wave amplitude estimates significantly.

Abstract

We characterize the post-inflationary evolution of the equation of state of the universe from the end of inflation until the onset of radiation domination, when the inflaton is coupled to a daughter field through a trilinear interaction. We consider an inflaton potential that is quadratic near the minimum and flattens in the inflationary regime. By simulating the dynamics in 2+1-dimensional lattices, we have tracked the long-term evolution of the equation of state for about ten e-folds of expansion, for various coupling strengths. The trilinear interaction initially excites daughter field modes through a process of tachyonic resonance immediately after inflation and triggers a temporary deviation of the equation of state from $\bar{w} = 0$ to a maximum value $\bar{w} = \bar{w}_{\rm max} < 1/3$. However, at much later times, the inflaton homogeneous mode once again dominates the energy density, pushing the equation of state towards $\bar{w} = 0$ until the onset of perturbative reheating. By combining the lattice results with a Boltzmann approach, we characterize the entire post-inflationary expansion history, which allows to calculate precise predictions for the inflationary CMB observables. We also accurately compute the redshift of the stochastic gravitational wave background produced during preheating, and show that taking the temporary return of the equation of state towards $\bar{w} = 0$ into account can reduce the amplitude by many orders of magnitude relative to previous estimates.