Geometric reheating of the Universe

We study the post-inflationary energy transfer from the inflaton ($\phi$) into a scalar field ($\chi$) non-minimally coupled to gravity through $\xi R|\chi|^2$, considering models with inflaton potential $V_{\rm inf} \propto |\phi|^{\,p}$ around $\phi = 0$. This corresponds to the paradigm of {\it geometric preheating}, which we extend to its non-linear regime via lattice simulations. Considering $\alpha$-attractor T-model potentials as a proxy, we study the viability of proper {\it reheating} for $p=2, 4, 6$, determining whether radiation domination (RD) due to energetic dominance of $\chi$ over $\phi$, can be achieved. For large inflationary scales $\Lambda$, reheating is frustrated for $p = 2$, it can be partially achieved for $p = 4$, and it becomes very efficient for $p = 6$. Efficient reheating can be however blocked if $\chi$ sustains self-interactions (unless these are extremely feeble), or if $\Lambda$ is low enough, so that inflaton fragmentation brings the universe rapidly into RD. Whenever RD is achieved, either due to reheating or to inflaton fragmentation, we characterize the energy and time scales of the problem, as a function of $\Lambda$ and $\xi$.