Non-minimal geometry–matter couplings in Weyl–Cartan space–times: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e1253" altimg="si4.svg"><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>,</mml:mo><mml:mi>Q</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> gravity

Harkó, Tiberiu; Myrzakulov, N.; Myrzakulov, Ratbay

doi:10.1016/j.dark.2021.100886

Cited by 33 publications

(10 citation statements)

References 152 publications

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“…. , VIII) [51][52][53], is F (R, T, Q, T ) gravity, corresponding to MG-VIII. The other are subcases.…”

Section: On-shell Equivalence To Vector-tensor Theoriesmentioning

confidence: 99%

Metric-Affine Vector-Tensor Correspondence and Implications in $F(R,T,Q,\mathcal{T},\mathcal{D})$ gravity

Iosifidis,

Myrzakulov,

Ravera

et al. 2021

Preprint

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We extend the results of antecedent literature on quadratic Metric-Affine Gravity by studying a new quadratic gravity action in vacuum which, besides the usual (non-Riemannian) Einstein-Hilbert contribution, involves all the parity even quadratic terms in torsion and non-metricity plus a Lagrangian that is quadratic in the field-strengths of the torsion and non-metricity vector traces. The theory result to be equivalent, on-shell, to a Vector-Tensor theory. We also discuss the sub-cases in which the contribution to the Lagrangian quadratic in the field-strengths of the torsion and non-metricity vectors just exhibits one of the aforementioned quadratic terms. We then report on implications of our findings in the context of F (R, T, Q, T , D) gravity.

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“…. , VIII) [51][52][53], is F (R, T, Q, T ) gravity, corresponding to MG-VIII. The other are subcases.…”

Section: On-shell Equivalence To Vector-tensor Theoriesmentioning

confidence: 99%

Metric-Affine Vector-Tensor Correspondence and Implications in $F(R,T,Q,\mathcal{T},\mathcal{D})$ gravity

Iosifidis,

Myrzakulov,

Ravera

et al. 2021

Preprint

Self Cite

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“…One of the possible extensions of general relativity is represented by theories that imply a geometry-matter coupling [77][78][79]. For extensive reviews and discussions of theories with geometry-matter coupling see [80][81][82][83][84][85]. Such a geometrical-physical approach leads to gravitational models more complicated than standard general relativity, and they represent an interesting possibility for explaining the accelerating expansion of the Universe, dark energy, and dark matter, respectively.…”

Section: Introductionmentioning

confidence: 99%

Coupling matter and curvature in Weyl geometry: conformally invariant $$f\left( R,L_m\right) $$ gravity

Harkó

2022

Eur. Phys. J. C

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We investigate the coupling of matter to geometry in conformal quadratic Weyl gravity, by assuming a coupling term of the form $$L_m{\tilde{R}}^2$$ L m R ~ 2 , where $$L_m$$ L m is the ordinary matter Lagrangian, and $${\tilde{R}}$$ R ~ is the Weyl scalar. The coupling explicitly satisfies the conformal invariance of the theory. By expressing $${\tilde{R}}^2$$ R ~ 2 with the help of an auxiliary scalar field and of the Weyl scalar, the gravitational action can be linearized, leading in the Riemann space to a conformally invariant $$f\left( R,L_m\right) $$ f R , L m type theory, with the matter Lagrangian nonminimally coupled to the Ricci scalar. We obtain the gravitational field equations of the theory, as well as the energy–momentum balance equations. The divergence of the matter energy–momentum tensor does not vanish, and an extra force, depending on the Weyl vector, and matter Lagrangian is generated. The thermodynamic interpretation of the theory is also discussed. The generalized Poisson equation is derived, and the Newtonian limit of the equations of motion is considered in detail. The perihelion precession of a planet in the presence of an extra force is also considered, and constraints on the magnitude of the Weyl vector in the Solar System are obtained from the observational data of Mercury. The cosmological implications of the theory are also considered for the case of a flat, homogeneous and isotropic Friedmann–Lemaitre–Robertson–Walker geometry, and it is shown that the model can give a good description of the observational data for the Hubble function up to a redshift of the order of $$z\approx 3$$ z ≈ 3 .

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“…in Refs. [48,[51][52][53][54][55][56], where astrophysical and cosmological applications are considered to investigate the large-scale structures. Here we consider the f (R, T (n) ) function to find the linearized field equations and thus the GWs equation.…”

Section: Introductionmentioning

confidence: 99%

Linearized Field Equations and Extra Force in $f(R,{\bf T}^{(n)})$ Extended Gravity

Abedi¹,

Bajardi²,

Capozziello³

2022

Preprint

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We consider an extended theory of gravity with Lagrangian L = f (R, T (n) ), with T (n) being a 2n-th order invariant made of contractions of the energy-momentum tensor. When n = 1 this theory reduces to f (R, T ) gravity, where T accounts for the trace of the energy-momentum tensor. We study the gravitational wave polarization modes, from which it results that when the matter Lagrangian contains dynamical scalar fields minimally coupled to the geometry, further polarization modes arise with respect to General Relativity. Finally we show that the motion for test particles is non-geodesic and we explicitly obtain the extra-force.

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Non-minimal geometry–matter couplings in Weyl–Cartan space–times: f(R,T,Q,Tm) gravity

Cited by 33 publications

References 152 publications

Metric-Affine Vector-Tensor Correspondence and Implications in $F(R,T,Q,\mathcal{T},\mathcal{D})$ gravity

Metric-Affine Vector-Tensor Correspondence and Implications in $F(R,T,Q,\mathcal{T},\mathcal{D})$ gravity

Coupling matter and curvature in Weyl geometry: conformally invariant $$f\left( R,L_m\right) $$ gravity

Linearized Field Equations and Extra Force in $f(R,{\bf T}^{(n)})$ Extended Gravity

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