  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 $r$.
