The cosmological significance of boundary term in non-metricity gravity

TL;DR

This paper explores the role of boundary terms in symmetric teleparallel gravity models with non-metricity, revealing their potential to explain early universe accelerated expansion.

Contribution

It introduces a new class of $f(Q,C)$ gravity models and demonstrates how boundary terms influence cosmological solutions, especially early accelerated expansion.

Findings

Boundary terms can induce early accelerated expansion.

Models with $f(Q,C)=Q^{s}+eC^{r}$ exhibit diverse cosmological behaviors.

Boundary terms are physically significant and should not be neglected.

Abstract

Within the context of metric-affine gravity, we examine the significance of the boundary term in symmetric teleparallel gravity by employing the cosmological dynamical system analysis method. We focus on the novel gravity models characterized by the functions $f(Q,C)$, where $f$ is a smooth function of the non-metricity scalar $Q$ and the associated boundary term $C$. In a cosmological setting adopting three different classes of symmetric teleparallel affine connections, we investigate a model $f(Q,C)=Q^{s}+eC^{r}$, and some special cases of this model. We show that the boundary term which is added to the Einsteinian field equations (or equivalently to $f(Q)=Q$ ones) are capable of bringing forward solutions corresponding to the early accelerated expansion. This alludes the physics behind the boundary terms which usually are discarded in the most gravitational theories.