Characterizing the postinflationary reheating history: Single daughter field with quadratic-quadratic interaction

We study the evolution of energy distribution and equation state Universe from end inflation until onset either radiation domination (RD) or a transient period matter (MD). use both analytical techniques lattice simulations. consider two-field models where inflaton $\Phi$ has monomial potential after $V(\Phi) \propto |\Phi - v|^p$ ($p\geq2$), is coupled to daughter field $X$ through quadratic-quadratic interaction $g^2\Phi^2 X^2$. two situations, depending on whether minimum at $i)$ $v = 0$, $ii)$ > 0$. In scenario $i)$, final transferred independent $g^2$ entirely determined by $p$: it negligible for $p < 4$, order $\sim 50\%$ \geq 4$. The system goes MD late times 2$, while RD 2$. later case, we can calculate exactly number e-folds as function $g^2$, hence predict accurately inflationary observables like scalar tilt $n_s$ tensor-to-scalar ratio $r$. $ii)$, always completely $p>2$, long its effective mass $m_X^2 g^2(\Phi-v)^2$ not negligible. For $p=2$, between densities depends strongly $g^2$. all \ge times.