On inflationary arctangent potentials and dark energy

In this paper, we investigate a square arctangent potential characterized by +a parameter [Formula: see text] and having a T-form. We apply the slow-roll approximation to derive various spectrum inflationary parameters and show that the slow-roll parameters depend only on the e-folding number [Formula: see text] and the parameter [Formula: see text]. We have found that the scalar spectral index [Formula: see text] rapidly converges toward the central value [Formula: see text], and the tensor-to-scalar r decreases to small values [Formula: see text]. We thus cover the main part of the plan [Formula: see text] of the observed cosmic microwave background by Planck experiment. Furthermore, we show that all inflationary perturbation parameters are compatible with the latest observational measurements and investigate the possible connection of the inflation field with dark energy.