Abstract: We study the energy distribution and equation of state of the universe between the end of inflation and the onset of radiation domination (RD), considering observationally consistent single-field inflationary scenarios, with a potential 'flattening' at large field values, and a monomial shape V(phi) proportional to vertical bar phi vertical bar(p) around the origin. As a proxy for (p)reheating, we include a quadratic interaction g(2)phi X-2(2) between the inflaton phi and a light scalar 'daughter' field X, with g(2) > 0. We capture the non-perturbative and non-linear nature of the system dynamics with lattice simulations, obtaining that: i) the final energy transferred to X depends only on p, not on g(2); ii) the final transfer of energy is always negligible for 2 <= p < 4, and of order similar to 50% for p >= 4; iii) the system goes at late times to matter-domination for p = 2, and always to RD for p > 2. In the latter case we calculate the number of e-folds until RD, significantly reducing the uncertainty in the inflationary observables Tl-s and r.