Physics

Gravitation

Classical field theory

Mathematics

Mathematical physics

Torsion (gastropod)

Scalar field

Scalar theories of gravitation

Scalar curvature

General relativity

Surgery

Dark energy

Curvature

Geometry

Cosmology

Theoretical physics

Quantum mechanics

Conformal map

Scalar (mathematics)

Medicine

Classical mechanics

Physical review. D/Physical review. D.

Einstein's celebrated theory of gravitation can be presented in three forms: general relativity, teleparallel gravity, and the rarely considered before symmetric teleparallel gravity. Extending the latter, we introduce a new class of theories where a scalar field is coupled nonminimally to nonmetricity $Q$, which here encodes the gravitational effects like curvature $R$ in general relativity or torsion $T$ in teleparallel gravity. We point out the similarities and differences with analogous scalar-curvature and scalar-torsion theories by discussing the field equations, role of connection, conformal transformations, relation to $f(Q)$ theory, and cosmology. The equations for a spatially flat universe coincide with those of teleparallel dark energy, thus allowing us to explain accelerating expansion.

Nonmetricity formulation of general relativity and its scalar-tensor extension