Friedmann equations in the Codazzi parametrization of Cotton and extended theories of gravity and the Dark Sector

TL;DR

This paper introduces a unified framework using Friedmann equations in Cotton gravity to model various extended theories of gravity and the dark sector, simplifying their comparison and analysis.

Contribution

It presents a parametrization of extended gravity theories via the Codazzi tensor, enabling a unified approach to dark sector models within Friedmann equations.

Findings

Reproduces Friedmann equations of multiple gravity extensions with a single function.

Includes recent models like Conformal Killing and Mimetic gravity.

Accommodates models extending ΛCDM, such as CPL.

Abstract

The Friedmann equations of Cotton gravity provide a simple parametrization to reproduce, by tuning a single function, the Friedmann equations of several extensions of gravity, such as f(R), modified Gauss-Bonnet f(G), teleparallel f(T), and more. It also includes the recently proposed Conformal Killing gravity and Mimetic gravity in FRW space-times. The extensions generally have the form of a Codazzi tensor that may be associated to the dark sector. Fixing it by a suitable equation of state accomodates most of the postulated models that extend $\Lambda$CDM, as the Chevallier-Polarski-Lindler model.