Reheating Constraints to Inflationary Models

Evidence from the BICEP2 experiment for a significant gravitational-wave background has focused attention on inflaton potentials V(ϕ)∝ϕ(α) with α = 2 ("chaotic" or "m(2)ϕ(2)" inflation) or with smaller values of α, as may arise in axion-monodromy models. Here we show that reheating considerations may provide additional constraints to these models. The reheating phase preceding the radiation era is modeled by an effective equation-of-state parameter w(re). The canonical reheating scenario is then described by w(re) = 0. The simplest α = 2 models are consistent with w(re) = 0 for values of n(s) well within the current 1σ range. Models with α = 1 or α = 2/3 require a more exotic reheating phase, with -1/3 1/3, unless n(s) is close to the lower limit of the 2σ range. For m(2)ϕ(2) inflation and canonical reheating as a benchmark, we derive a relation log(10)(T(re)/10(6) GeV) ≃ 2000(n(s)-0.96) between the reheat temperature T(re) and the scalar spectral index n(s). Thus, if n(s) is close to its central value, then T(re) ≲ 10(6) GeV, just above the electroweak scale. If the reheat temperature is higher, as many theorists may prefer, then the scalar spectral index should be closer to n(s) ≃ 0.965 (at the pivot scale k = 0.05 Mpc(-1)), near the upper limit of the 1σ error range. Improved precision in the measurement of n(s) should allow m(2)ϕ(2), axion monodromy, and ϕ(40) models to be distinguished, even without precise measurement of r, and to test the m(2)ϕ(2) expectation of n(s) ≃ 0.965.