Energy distribution and equation of state of the early Universe:
  matching the end of inflation and the onset of radiation domination
  We study the energy distribution and equation of state of the universe
between the end of inflation and the onset of radiation domination (RD),
considering observationally consistent single-field inflationary scenarios,
with a potential 'flattening' at large field values, and a monomial shape
$V(\phi) \propto |\phi|^p$ around the origin. As a proxy for (p)reheating, we
include a quadratic interaction $g^2\phi^2X^2$ between the inflaton $\phi$ and
a light scalar 'daughter' field $X$, with $g^2>0$. We capture the
non-perturbative and non-linear nature of the system dynamics with lattice
simulations, obtaining that: $i)$ the final energy transferred to $X$ depends
only on $p$, not on $g^2$, ; $ii)$ the final transfer of energy is always
negligible for $2 \leq p < 4$, and of order $\sim 50\%$ for $p \geq 4$; $iii)$
the system goes at late times to matter-domination for $p = 2$, and always to
RD for $p > 2$. In the latter case we calculate the number of e-folds until RD,
significantly reducing the uncertainty in the inflationary observables $n_s$
and $r$.
