Constraints on α-attractor inflation and reheating

We investigate a constraint on reheating followed by alpha-attractor-type inflation (the E-model and T-model) from an observation of the spectral index n(s). When the energy density of the Universe is dominated by an energy component with the cosmic equation-of-state parameter w(re) during reheating, its e-folding number N-re and the reheating temperature T-re are bounded depending on w(re). When the reheating epoch consists of two phases-where the energy density of the Universe is dominated by uniform inflaton field oscillations in the first phase and by relativistic nonthermalized particles in the second phase-we find a constraint on the e-folding number of the first oscillation phase, N-sc, depending on the parameters of the inflaton potential. For the simplest perturbative reheating scenario, we find the lower bound for a coupling constant of inflaton decay in the E-model and T-model depending on the model parameters. We also find a constraint on the a parameter, alpha >= 0.01, for the T-model and E-model when we assume a broad resonance