Nonmetricity formulation of general relativity and its scalar-tensor extension

By L. Jarv, Mihkel Runkla, M. Saal, O. Vilson. Physical Review D, 2018

151 citations recorded by the source corpus.

Einstein's celebrated theory of gravitation can be presented in three forms: general relativity, teleparallel gravity, and the rarely considered before symmetric teleparallel gravity. These formulations differ in the underlying geometric structure and interpretations, but are equivalent in observational predictions. The theories truly part when one extends them by e.g. nonminimally coupling a scalar field to the metric tensor degree of freedom. Thus extending symmetric teleparallel gravity, 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 derive the field equations and point out the similarities and differences with analogous scalar-curvature and scalar-torsion theories. We show that while scalar-nonmetricity gravity lacks invariance under conformal transformations, a suitable extra term can restore this; and also establish that $f(Q)$ gravity forms a particular subclass of scalar-nonmetricity theories. We illustrate the theory with an example of flat Friedmann-Lema\^{\i}tre-Robertson-Walker spacetime.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/c7cef14a468c2f41b6487cf69d3305e56bf6c79b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Nuclear and High Energy Physics

Citations in the corpus

Teleparallel theories of gravity: illuminating a fully invariant approach (2018, background): “Within this framework it is possible to formulate the symmetric teleparallel equivalent of general relativity [145–149], which can be understood also as a gauge theory for translations [150, 151], and construct new modified gravity models [95, 152–155].”
Cosmological solutions and growth index of matter perturbations in f(Q) gravity (2021, background): “[17] Laur Järv, Mihkel Rünkla, Margus Saal, and Ott Vilson, “Nonmetricity formulation of general relativity and its scalartensor extension,” Phys.”
Modified Gravity and Cosmology (2021, unknown): “In particular, using that a general connection Γ̂μν can be decomposed as [25]:”
Teleparallel Palatini theories (2018, background): “Some systematic studies are presently undertaken to explore scalar-torsion theories in teleparallelism [108–111], and the first step into STG was just taken by introducing Brans-Dicke-type coupling of a scalar field and the Q-scalar [112].”