Speed of sound and scalar spectral index: Reconstructing inflation and reheating in a non-canonical theory

Abstract

In this article we analyze the reconstruction of inflation in the framework of a non-canonical theory. In this sense, we study the viability of reconstructing the background variables assuming a non-linear kinetic term given by K(X,ϕ)=X+g(ϕ)X2, with X the standard kinetic term associated to the scalar field ϕ and g(ϕ) an arbitrary coupling function. In order to achieve this reconstruction in the context of inflation, we assume the slow-roll approximation together with the parametrization of the scalar spectral index ns and the speed of sound cs as a function of the number of e−folds N. By assuming the simplest parametrizations for ns−1=−2/N and cs∝N−β with β a constant, we find the reconstruction of the effective potential V(ϕ) and the coupling function g(ϕ) in terms of the scalar field. Besides, we study the reheating epoch by considering a constant equation of state parameter, where we determine the temperature and number of e−folds during the reheating epoch in terms of the reconstructed variables and the observational parameters. In this way, the parameter-space related to the reconstructed inflationary model are constrained during the epochs of inflation and reheating by assuming the current astronomical data from Planck and BICEP/Keck results.