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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 (ϕ) ∝ | ϕ | p around the origin. As a proxy for (p)reheating, we include a quadratic interaction g 2 ϕ 2 X 2 between the inflaton ϕ 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 ; i i) the final transfer of energy is always negligible for 2 ≤ p < 4 , and of order ∼ 50 % for p ≥ 4 ; i i i) 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 n s and r. [ABSTRACT FROM AUTHOR]