Family of scalar-nonmetricity theories of gravity

TL;DR

This paper introduces a broad family of scalar-nonmetricity gravity theories by coupling a five-parameter nonmetricity scalar with a scalar field, extending previous models and deriving their field equations.

Contribution

It generalizes scalar-nonmetricity theories by including multiple parameters and mixed kinetic terms, providing a comprehensive framework that encompasses general relativity and scalar-tensor theories.

Findings

Derived the field equations for the new class of theories.

Established the equivalence to general relativity and scalar-tensor theories as special cases.

Developed a Hamilton-like formulation for the theories.

Abstract

We extend the class of recently formulated scalar-nonmetricity theories by coupling a five-parameter nonmetricity scalar to a scalar field and considering a mixed kinetic term between the metric and the scalar field. The symmetric teleparallel constraint is invoked by Lagrange multipliers or by inertial variation. The equivalents for the general relativity and ordinary (curvature-based) scalar-tensor theories are obtained as particular cases. We derive the field equations, discuss some technical details, e.g., debraiding, and formulate the Hamilton-like approach.