Formation and decay of oscillons after inflation in the presence of an external coupling, Part-I: Lattice simulations

We investigate the formation and decay of oscillons during the post-inflationary reheating epoch from inflaton oscillations around asymptotically flat potentials $V(\varphi)$ in the presence of an external coupling of the form $\frac{1}{2}\, g^2 \, \varphi^2 \, \chi^2$. It is well-known that in the absence of such an external coupling, the attractive self-interaction term in the potential leads to the formation of copious amounts of long-lived oscillons both for symmetric and asymmetric plateau potentials. We perform a detailed numerical analysis to study the formation of oscillons in the $\alpha$-attractor E- and T-model potentials using the publicly available lattice simulation code ${\cal C}$osmo${\cal L}$attice. We observe the formation of nonlinear oscillon-like structures with the average equation of state $\langle w_\varphi\rangle \simeq 0$ for a range of values of the inflaton self-coupling $\lambda$ and the external coupling $g^2$. Our results demonstrate that oscillons form even in the presence of an external coupling and we determine the upper bound on $g^2$ which facilitates oscillon formation. We also find that eventually, these oscillons decay into the scalar inflaton radiation as well as into the quanta of the offspring field $\chi$. Thus, we establish the possibility that reheating could have proceeded through the channel of oscillon decay, along with the usual decay of the oscillating inflaton condensate into $\chi$ particles. For a given value of the self-coupling $\lambda$, we notice that the lifetime of a population of oscillons decreases with an increase in the strength of the external coupling, following an (approximately) inverse power-law dependence on $g^2$.