# A novel non-metricity extension of scalar-tensor gravity in spatially curved spacetime

## TL;DR

This paper explores a new scalar-tensor gravity theory based on non-metricity geometry in curved spacetime, analyzing its cosmological dynamics and stability, and showing it can produce realistic cosmic evolution including late-time acceleration.

## Contribution

It introduces a novel non-metricity extension of scalar-tensor gravity, analyzing its critical points and stability in spatially curved FLRW spacetimes using dynamical systems methods.

## Key findings

- Existence of matter-dominated and de Sitter solutions
- Stable late-time accelerated attractors identified
- Scalar field dynamics significantly influence cosmological evolution

## Abstract

We investigate a non-minimally coupled scalar field theory within the framework of scalar-tensor gravity formulated in non-metricity geometry, focusing on spatially curved FLRW spacetimes. Employing the dynamical systems approach with Hubble-normalized variables, we reformulate the field equations into an autonomous system and analyze the resulting critical points. Four distinct cases, determined by the scalar coupling and potential functions, are studied in detail. For each case, we identify the existence and stability of equilibrium points, classify their cosmological behavior, and compute key observables such as the deceleration parameter and effective equation of state. Our results reveal that the theory admits matter-dominated eras, parameter-dependent saddle solutions, and stable de Sitter attractors capable of driving late-time cosmic acceleration. The additional scalar degree of freedom introduced by the non-coincident gauge plays a crucial role in determining the system's dynamics and viability. These findings emphasize the potential of scalar-tensor non-metricity gravity as a robust extension of general relativity and motivate further confrontation of the model with observational data.