On the α-attractor T-models

We carry out a fully analytical study of the phenomenology of α-attractor T-models defined by the potential V = V₀tanh^p(λϕ/M_pl). We obtain expressions for the number of e-folds during inflation N_ke in terms of the scalar spectral index n_s and independently in terms of the tensor-to-scalar ratio r. From these expressions we obtain exact solutions for both n_s and r in terms of N_ke along with their expansions for large N_ke, in full agreement with known expressions. Eliminating the parameter λ from the model in terms of n_s and r we can obtain exact solutions for r in terms of n_s and N_ke which allows us to reproduce, in particular, numerical solutions presented by the Planck Collaboration for the monomial potentials. We explicitly show how these solutions are contained in the solutions for the α-attractors and are also the end points of these. Finally, by also eliminating the global scale V₀ in terms of the observables n_s and r we show how in the appropriate limit the α-attractor potential exactly reduces to the monomials potential. We also briefly show that for α-attractor E-models, which generalize the Starobinsky potential in the Einstein frame, a similar transition occurs. (paper)