Abstract

Inspired by the reconstruction scheme of the inflaton field potential V(phi) from the attractors n(s)(N), we investigate the viability of reconstructing the inflationary potential within the framework of k-inflation for a non-linear kinetic term K(X) = k(n+1)X(n) through three expressions for the scalar spectral index n(s)(N), namely: (i) n(s) - 1 = - 2/N, (ii) n(s) - 1 = -p/N, and (iii) n(s) - 1 = -beta/N-q. For each reconstructed potential, we determine the values of the parameter space which characterizes it by requiring that it must reproduce the observable parameters from PLANCK 2018 and BICEP/Keck results. Furthermore, we analyze the reheating era by assuming a constant equation of state, in which we derive the relations between the reheating duration, the temperature at the end of reheating together with the reheating epoch, and the number of..-folds during inflation. In this sense, we unify the inflationary observables in order to narrow the parameter space of each model within the framework of the reconstruction in k-inflation.