Can an Extra Degree of Freedom in Scalar-Tensor Non-Metricity Gravity Account for the Evolution of the Universe?

TL;DR

This paper explores how an extra scalar degree of freedom in scalar-tensor non-metricity gravity can model the universe's expansion history, revealing new regimes and potential observational signatures beyond standard cosmology.

Contribution

It demonstrates that the additional scalar degree of freedom can replicate and extend the standard cosmological evolution, introducing novel late-time and high-curvature behaviors.

Findings

Reinstates the $\\Lambda$CDM sequence with suitable parameters

Identifies new late-time and high-curvature regimes from non-metricity

Highlights potential observational differences from metric scalar-tensor theories

Abstract

We investigate whether the extra scalar degree of freedom that arises in the second connection class of scalar-tensor non-metricity gravity can accurately replicate and potentially enrich the cosmic expansion history. Focusing on a spatially flat FLRW background, we introduce Hubble-normalized variables and recast the field equations into an autonomous dynamical system. Four representative scenarios are analyzed comprehensively. Phase-space research reveals a rich hierarchy of critical points: matter-dominated, stiff-fluid, and de Sitter solutions, together with asymptotic trajectories leading to Big-Crunch/Rip singularities and transient, unstable matter epochs. With suitable parameter choices, the standard $\Lambda$CDM sequence is reinstated; however, novel late-time and high-curvature regimes arise exclusively from the non-metricity sector. A systematic comparison of metric scalar-tensor and teleparallel scalar-torsion theories reveals unique stability characteristics and potential observational discriminants. Our findings indicate that the additional time-dependent function inherent to scalar-tensor non-metricity gravity can effectively explain the Universe's evolution while providing new phenomenology that can be tested by upcoming surveys.