Scalar field coupled to boundary in non-metricity: a new avenue towards dark energy

TL;DR

This paper introduces a new scalar-tensor gravity model with boundary term coupling in non-metricity, offering a promising geometric approach to explain late-time cosmic acceleration.

Contribution

It proposes a novel non-metricity scalar-tensor theory with boundary term coupling that recovers STEGR and explores its cosmological implications.

Findings

Standard thermal histories are recovered.

Stable de Sitter attractors are identified.

The model provides a flexible geometric framework for dark energy.

Abstract

While conformal transformations in metric scalar-tensor theories recover General Relativity, this feature is notably absent in standard non-metricity-based theories. We demonstrate that by introducing the boundary term C, a non-metricity scalar-tensor theory can recover Symmetric Teleparallel Equivalent of General Relativity (STEGR) in the Einstein frame. Motivated by this, we propose a novel gravity model where a scalar field couples nonminimally to both the non-metricity scalar Q and the boundary term C. We focus in the cosmological scenario where we present the covariant formulation and a unified autonomous system framework that treats generic affine-connection choices, including coincident and non-coincident gauges, on an equal footing. Our dynamical analysis across three connection branches reveals standard thermal histories and stable de Sitter attractors. These results show that boundary-term couplings provide a well-posed, geometrically flexible route to addressing late-time cosmic acceleration.