Post-Newtonian limit of generalized symmetric teleparallel gravity

Abstract

In this article we analyze the post-Newtonian approximation of a generalization of the symmetric teleparallel gravity with the help of the parameterized post-Newtonian (PPN) formalism. This class of theories is based on a free function of the five independent quadratic contractions of the non-metricity tensor. By calculating the PPN metric of these theories, we can restrict the Taylor coefficients of the free function with the help of the PPN parameters and their observational bounds. We find two families of theories whose PPN parameters are identical to those of general relativity, and thus in full agreement with observations. For three further families, we find that only the PPN parameters β and γ deviate, but can be brought arbitrarily close to their general relativity values by an appropriate choice of the Lagrangian, so that also these families contain candidate theories which agree with observations. The remaining theories either possess no well-defined solution of the post-Newtonian field equations, or possess a post-Newtonian limit which exceeds the form assumed in the PPN formalism.

Post-Newtonian limit of generalized scalar-torsion theories of gravity

“…(4). As developed in [35], we expand the coordinates around the coordinates of the coincident gauge up to quadratic orders of the generators of a "knight diffeomorphism"…”

“…In this article we make use of the PPN formalism in order to derive the post-Newtonian limit of a general class of scalar-nonmetricity theories of gravity, which generalizes the originally proposed class [27], following a similar idea as applied in scalar-torsion gravity [25], and allowing for a gravitational action defined by an arbitrary function of the nonmetricity scalar, two non-minimal coupling terms, the scalar field and its kinetic energy, and which we will therefore denote L(Q, X, Y, Z, φ) theories of gravity. For this purpose, we make use of the previously developed post-Newtonian expansion of symmetric teleparallel gravity theories [35,36], which we enhance by including a post-Newtonian expansion for the scalar field and a Taylor expansion for the free function defining the action, in full analogy to the case of scalar-torsion gravity [37]. Our conventions and notation follow the textbook [33].…”

xPPN: an implementation of the parametrized post-Newtonian formalism using xAct for Mathematica

“…Finally, the vector field is expanded in velocity orders. It turns out that in the PPN formalism the only non-vanishing components are given by [25] 2…”

Accidental Gauge Symmetries of Minkowski Spacetime in Teleparallel Theories

“…However, most of these studies, including the one at hand, focus on non-linear modifications of the teleparallel equivalents of GR (which, from the perspective of teleparallelism as the low-energy manifestation of the ultra-massive spacetime connection, could perhaps be interpreted as non-linear extensions of the quadratic Proca-like term) which have been mainly motivated by their potential use as models of cosmological inflation and dark energy (and even dark matter [6,7]). The non-linear extension of TEGR, the f (T) theory [8], has been considered in, e.g., [9][10][11][12][13][14][15][16][17][18], and the non-linear extension of STEGR, the f (Q) [4] and related theories have been considered in, e.g., [19][20][21][22][23][24][25][26][27][28]. The general teleparallel equivalent of GR, not subject to either the metric or the symmetric condition, was introduced quite recently [29], and only in this paper do we take some first steps towards understanding the properties of the non-linearly extended f (G) theory.…”

“…The theory in this gauge defines the STEGR or Coincident GR (alluding to the gauge choice) and is described by the non-metricity scalar Q =G(T α µν = 0). Non-linear extensions based on the above two gauge choices [4,8] have been considered in the literature at some length [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. Regarding these generalisations, it is important to notice that the presence of the different boundary terms is what makes the non-linear extensions based on different gauge choices give rise to different theories.…”