Constraining α-attractor models from reheating

In this paper, we eliminate the parameters originally present in models of inflation of the alpha-attractor type in favor of the scalar spectral index n(s) and the tensor-to-scalar ratio r. We then write expressions for the number of e-folds during reheating N-re. By imposing reasonable conditions on N-re, we can restrict n(s) and r and in turn, we use these constraints in order to find bounds for cosmological quantities of interest such as the number of e-folds during inflation and the radiation dominated eras, as well as for the reheating temperature and the running index. The minimum condition that N-re must satisfy is N-re >= 0 which we use to constrain the cosmological quantities mentioned above. In particular, we find that the tensor-to-scalar ratio r (and as a consequence the energy scale of inflation) is bounded from below. We provide figures illustrating the behavior of these quantities as functions of r for several values of n(s) and tables containing the bounds so obtained.