From inflation to dark energy in scalar-tensor cosmology

The methods of dynamical systems have found wide applications in cosmology, with focus either upon inflation or upon the passage into dark energy era. In this paper, we endeavor to capture the whole history of the universe into a dynamical system by considering generic scalar tensor gravity with radiation and dust matter fluids in flat Friedmann-Lemaitre-Robertson-Walker spacetime. We construct the dynamical variables in such a way that the main stages of the cosmic evolution, viz. inflation, radiation domination, matter domination, and dark energy domination can be represented by the respective fixed points in the phase space. As the evolution of solutions is ruled by the sequence of these fixed points with appropriate properties, we can determine the conditions that the scalar potential and nonminimal coupling must satisfy for the model to deliver viable cosmic history in a generic manner. We illustrate the construction by a scalar field with quartic potential, with and without quadratic nonminimal coupling to curvature.