Oscillon formation from preheating in asymmetric inflationary potentials

We investigate the possibility of oscillon formation during the preheating phase of asymmetric inflationary potentials. We analytically establish the existence of oscillon-like solutions for the Klein-Gordon equation for a polynomial potential of the form $V(\phi)=\frac{1}{2}\phi^2+A\phi^3+B\phi^4$ using the small amplitude analysis, which naturally arises as a Taylor expansion of the $\alpha$-attractor E-model for $\phi\ll M_\text{pl}$ and $\alpha\sim\mathcal{O}(1)$. We perform a detailed numerical analysis to study the formation of nonlinear structures in the $\alpha$-attractor E-model using the publicly available lattice simulation code $\mathcal{C}\text{osmo}\mathcal{L}\text{attice}$ for parameters in the range $10^{-5}\lesssim\alpha\lesssim 5\times 10^{-4}$. We find the backreaction of the field fluctuations onto the evolution of the homogeneous inflaton condensate to be significant for $\alpha\lesssim 2\times 10^{-4}$ for which we observe the formation of highly nonlinear structures with average equation of state $w\simeq 0$. These nonlinear structures maybe interpreted as oscillons, providing evidence that they can form during the inflaton oscillations around an asymmetric potential and are found to be present for the entirety of the runtime of our simulations, comprising $\gtrsim 40\%$ of the total energy density.