The Equation of State and Duration to Radiation Domination After
  Inflation
  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, $V(\phi)\propto |\phi|^{2n}$ near the
origin, and where the couplings to other fields are ignored are included in our
analysis. We find that the equation of state parameter $w\rightarrow 0$ for
$n=1$ and $w\rightarrow 1/3$ (after sufficient time) for $n\gtrsim 1$. We
calculate how the number of $e$-folds to radiation domination depends on both
$n$ and $M$ when $M\sim m_{\rm pl}$, whereas when $M\ll m_{\rm pl}$, 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,
scaling arguments, and are supported by detailed 3+1 dimensional lattice
simulations. We show how our work significantly reduces the uncertainty in
inflationary observables, even after including couplings to additional light
fields.
