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