Geodesic deviation, Raychaudhuri equation, Newtonian limit, and tidal forces in Weyl-type f(Q, T) gravity

Yang, Jinzhao; Shahidi, Shahab; Harkó, Tiberiu; Liang, Shi‐Dong

doi:10.1140/epjc/s10052-021-08910-6

“…An interesting approach based on Weyl geometry is the so-called symmetric teleparallel gravity approach, in which the gravitational field is described by the nonmetricity alone [16]. This approach was extended in the form of the f (Q) theory in [17], where Q is the nonmetricity scalar, and further analyzed and extended in [18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Cosmological evolution and dark energy in osculating Barthel–Randers geometry

Hama

¹

,

Harkó

²

,

Sabau

³

2021

Self Cite

View full text Add to dashboard Cite

We consider the cosmological evolution in an osculating point Barthel–Randers type geometry, in which to each point of the space-time manifold an arbitrary point vector field is associated. This Finsler type geometry is assumed to describe the physical properties of the gravitational field, as well as the cosmological dynamics. For the Barthel–Randers geometry the connection is given by the Levi-Civita connection of the associated Riemann metric. The generalized Friedmann equations in the Barthel–Randers geometry are obtained by considering that the background Riemannian metric in the Randers line element is of Friedmann–Lemaitre–Robertson–Walker type. The matter energy balance equation is derived, and it is interpreted from the point of view of the thermodynamics of irreversible processes in the presence of particle creation. The cosmological properties of the model are investigated in detail, and it is shown that the model admits a de Sitter type solution, and that an effective cosmological constant can also be generated. Several exact cosmological solutions are also obtained. A comparison of three specific models with the observational data and with the standard $$\Lambda $$ Λ CDM model is also performed by fitting the observed values of the Hubble parameter, with the models giving a satisfactory description of the observations.

show abstract

“…Derivative matter couplings are also considered in [140,141], where the Galileon interactions are promoted to contain matter Lagrangians. Nonminimal couplings between nonmetricity and matter were investigated in [142][143][144][145]. For reviews and detailed discussions on the gravitational theories with geometry-matter coupling see [146] and [147], respectively.…”

Section: (Mat) μνmentioning

confidence: 99%

Generalizing the coupling between geometry and matter: $$f\left( R,L_m,T\right) $$ gravity

Haghani

¹

,

Harkó

²

2021

Self Cite

View full text Add to dashboard Cite

We generalize and unify the $$f\left( R,T\right) $$ f R , T and $$f\left( R,L_m\right) $$ f R , L m type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R, of the trace of the energy–momentum tensor T, and of the matter Lagrangian $$L_m$$ L m , so that $$ L_{grav}=f\left( R,L_m,T\right) $$ L grav = f R , L m , T . We obtain the gravitational field equations in the metric formalism, the equations of motion for test particles, and the energy and momentum balance equations, which follow from the covariant divergence of the energy–momentum tensor. Generally, the motion is non-geodesic, and takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equations of motion is also investigated, and the expression of the extra acceleration is obtained for small velocities and weak gravitational fields. The generalized Poisson equation is also obtained in the Newtonian limit, and the Dolgov–Kawasaki instability is also investigated. The cosmological implications of the theory are investigated for a homogeneous, isotropic and flat Universe for two particular choices of the Lagrangian density $$f\left( R,L_m,T\right) $$ f R , L m , T of the gravitational field, with a multiplicative and additive algebraic structure in the matter couplings, respectively, and for two choices of the matter Lagrangian, by using both analytical and numerical methods.

show abstract

“…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.…”

Section: Introductionmentioning

confidence: 99%

“…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.…”

mentioning

confidence: 99%

Accidental Gauge Symmetries of Minkowski Spacetime in Teleparallel Theories

Jiménez

¹

,

Koivisto

²

2021

View full text Add to dashboard Cite

In this paper, we provide a general framework for the construction of the Einstein frame within non-linear extensions of the teleparallel equivalents of General Relativity. These include the metric teleparallel and the symmetric teleparallel, but also the general teleparallel theories. We write the actions in a form where we separate the Einstein–Hilbert term, the conformal mode due to the non-linear nature of the theories (which is analogous to the extra degree of freedom in f(R) theories), and the sector that manifestly shows the dynamics arising from the breaking of local symmetries. This frame is then used to study the theories around the Minkowski background, and we show how all the non-linear extensions share the same quadratic action around Minkowski. As a matter of fact, we find that the gauge symmetries that are lost by going to the non-linear generalisations of the teleparallel General Relativity equivalents arise as accidental symmetries in the linear theory around Minkowski. Remarkably, we also find that the conformal mode can be absorbed into a Weyl rescaling of the metric at this order and, consequently, it disappears from the linear spectrum so only the usual massless spin 2 perturbation propagates. These findings unify in a common framework the known fact that no additional modes propagate on Minkowski backgrounds, and we can trace it back to the existence of accidental gauge symmetries of such a background.

show abstract

Geodesic deviation, Raychaudhuri equation, Newtonian limit, and tidal forces in Weyl-type f(Q, T) gravity

Cited by 80 publications

References 102 publications

Cosmological evolution and dark energy in osculating Barthel–Randers geometry

Cosmological evolution and dark energy in osculating Barthel–Randers geometry

Generalizing the coupling between geometry and matter: $$f\left( R,L_m,T\right) $$ gravity

Accidental Gauge Symmetries of Minkowski Spacetime in Teleparallel Theories

Contact Info

Product

Resources

About