A unified model of dark energy and inflation from the Markov-Mukhanov action

Abstract: We propose a unified model of dark energy and inflation through the Markov-Mukhanov modification of the Einstein-Hilbert action, where the matter sector is coupled to gravity via a scalar coupling function depending only on the energy density of the matter content. We assume that the coupling function encodes the UV corrections to the standard model of cosmology and we determine the form of the coupling that allows for the dark energy component to be dynamical and act as the inflaton field in the early universe. Interestingly we show that our model, in order to account for inflation, prefers a dark energy equation of state with $w$ close but not equal to $-1$ in agreement with the latest DESI data.