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

TL;DR

We address late-time cosmic acceleration by extending scalar-tensor gravity to the non-metricity framework and coupling a scalar to the non-metricity scalar $Q$ and the boundary term $C$. Using a covariant formulation, the authors derive a unified autonomous dynamical system that is valid for multiple affine-connection branches $\Gamma_A$, $\Gamma_B$, $\Gamma_C$, enabling a global phase-space analysis. They show that a conformal transformation can bring the theory into an Einstein-frame STEGR, a feature absent in pure non-metricity theories, and identify stable de Sitter attractors and standard thermal histories across connection classes. The results indicate that boundary-term couplings provide a geometrically flexible route to late-time acceleration, with several parameter regimes supporting acceleration and a natural progression from matter domination to 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.

Figures (3)

• Figure 1: Qualitative evolution of the deceleration parameter for connection $\Gamma_A$ for different values of $\lambda_0$ and $\mu_0$, with initial conditions ($x_2[0]=0.1,~x_3[0]=0.3$) with parameter value is $h=0.5$.
• Figure 2: Qualitative evolution of the deceleration parameter for connection $\Gamma_B$ for different values of $\lambda_0$ and $\mu_0$, with initial conditions ($x_2[0]=0.1,~x_3[0]=0.1,~x_5[0]=0.1$) with parameter value is $h=0.5$.
• Figure 3: Qualitative evolution of the deceleration parameter for connection $\Gamma_C$ for different values of $\lambda_0$ and $\mu_0$, with initial conditions ($x_2[0]=0.8,~x_3[0]=0.01,~x_4[0]=0.05$) with parameter value is $h=0.5$.