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arXiv · 1802.00492

Nonmetricity formulation of general relativity and its scalar-tensor extension

Laur Järv·Mihkel Rünkla·Margus Saal·Ott Vilson
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Abstract

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 spatially flat universe coincide with those of teleparallel dark energy, thus allowing to explain accelerating expansion.

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Laur Järv, Mihkel Rünkla, Margus Saal, Ott Vilson. 2018-02-01. Nonmetricity formulation of general relativity and its scalar-tensor extension. https://doi.org/10.1103/physrevd.97.124025

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