Simple cosmological model with inflation and late times acceleration

TL;DR

This paper presents a simple polynomial Palatini cosmological model that naturally exhibits both early inflation and late-time acceleration, with dark energy modeled as a decaying scalar field interacting with matter.

Contribution

It introduces a covariant form of dark energy and matter parametrization based on the Ricci scalar, demonstrating inflation and acceleration within a unified framework.

Findings

Early inflation occurs at negligible matter density.

Dark energy density follows a logistic-like evolution over cosmic time.

Derived bounds on model parameters based on inflationary e-folds.

Abstract

In the framework of polynomial Palatini cosmology, we investigate a simple cosmological homogeneous and isotropic model with matter in the Einstein frame. We show that in this model during cosmic evolution, it appears the early inflation and the accelerating phase of the expansion for the late times. In this frame we obtain the Friedmann equation with matter and dark energy in the form of a scalar field with the potential whose form is determined in a covariant way by the Ricci scalar of the FRW metric. The energy density of matter and dark energy are also parametrized through the Ricci scalar. The early inflation is obtained only for an infinitesimally small fraction of energy density of matter. Between the matter and dark energy, there exists interaction because the dark energy is decaying. For characterization of inflation we calculate the slow roll parameters and the constant roll parameter in terms of the Ricci scalar. We have found a characteristic behaviour of the time dependence of density of dark energy on the cosmic time following the logistic-like curve which interpolates two almost constant value phases. From the required numbers of $N$-folds we have found a bound on model parameter.