Geometric acceleration in $f(Q,C)$ theories

TL;DR

This paper explores a new class of $f(Q,C)$ gravity models that modify cosmology by geometrically generating dark energy, proposing models that fit observations better than standard $ ext{ extLambda}$CDM.

Contribution

It introduces a general $f(Q,C)$ formulation with second-order equations, derives guidelines for cosmological models, and shows how to relate these to $f(Q)$ models at the background level.

Findings

A variant of the DGP model within $f(Q,C)$ is statistically favored over $ ext{ extLambda}$CDM.

The framework allows translating solutions to $f(Q)$ models at the background level.

New observationally supported evolving dark energy models are proposed.

Abstract

The $f(Q,C)$ framework of gravity enables the depiction of an effective dark energy fluid that emerges from geometry itself, thus leading to modifications in the cosmological phenomenology of General Relativity. We pursue this approach to discover new and observationally supported (effective) evolving dark energy models. We propose a general $f(Q,C)$ formulation that cannot be simply split into separate functions of $Q$ and $C$, yet it still results in second-order field equations. By employing a particular type of connection, we derive guidelines for new cosmological models, including a variant of the DGP model that appears to be statistically favored over $\Lambda$CDM. Notably, we also demonstrate how to translate solutions within this $f(Q,C)$ framework to $f(Q)$ counterparts at the background level.