Emergence of running dark energy from polynomial f(R) theory in Palatini formalism

Abstract

Abstract We consider FRW cosmology in $$f(R)= R+ \gamma R^2+\delta R^3$$ f ( R ) = R + γ R 2 + δ R 3 modified framework. The Palatini approach reduces its dynamics to the simple generalization of Friedmann equation. Thus we study the dynamics in two-dimensional phase space with some details. After reformulation of the model in the Einstein frame, it reduces to the FRW cosmological model with a homogeneous scalar field and vanishing kinetic energy term. This potential determines the running cosmological constant term as a function of the Ricci scalar. As a result we obtain the emergent dark energy parametrization from the covariant theory. We study also singularities of the model and demonstrate that in the Einstein frame some undesirable singularities disappear.