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-lineal 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.