The first variation of the matter energy-momentum tensor with respect to the metric, and its implications on modified gravity theories

Haghani, Zahra; Harkó, Tiberiu

doi:10.48550/arxiv.2301.12133

Cited by 2 publications

(2 citation statements)

References 26 publications

(36 reference statements)

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“…In line with the standard cosmological model, we consider DM as a perfect, pressureless fluid, with T µν DM = ρ u µ u ν and T DM = −ρ. In this case [41] have shown that, in standard astrophysical and cosmological settings, where the entropy and particle production rates remain unchanged during the dynamical evolution of the fluid, the variation of the trace of the stress energy tensor can be written in a closed form as…”

Section: Relativistic Action and Equations Of Motionmentioning

confidence: 99%

A relativistic scalar model for fractional interaction between dark matter and gravity

Benetti,

Lapi,

Gandolfi

et al. 2024

Class. Quantum Grav.

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In a series of recent papers we put forward a “fractional gravity”framework striking an intermediate course between a modified gravity theory and anexotic dark matter (DM) scenario, which envisages the DM component in virializedhalos to feel a non-local interaction mediated by gravity. The remarkable successof this model in reproducing several aspects of DM phenomenology motivates us tolook for a general relativistic extension. Specifically, we propose a theory, dubbedRelativistic Scalar Fractional Gravity or RSFG, in which the trace of the DM stressenergy tensor couples to the scalar curvature via a non-local operator constructed witha fractional power of the d’Alembertian. We derive the field equations starting froman action principle, and then we investigate their weak field limit, demonstrating thatin the Newtonian approximation the fractional gravity setup of our previous works isrecovered. We compute the first-order post-Newtonian parameter γ and its relationwith weak lensing, showing that although in RSFG the former deviates from its GRvalues of unity, the latter is unaffected. We also perform a standard scalar-vectortensor-decomposition of RSFG in the weak field limit, to highlight that gravitationalwaves propagate at the speed of light, though also an additional scalar mode becomesdynamical. Finally, we derive the modified conservation laws of the DM stress energytensor in RSFG, showing that a new non-local force emerges, and hence that the DMfluid deviates from the geodesic solutions of the field equations.

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Section: Relativistic Action and Equations Of Motionmentioning

confidence: 99%

A relativistic scalar model for fractional interaction between dark matter and gravity

Benetti,

Lapi,

Gandolfi

et al. 2024

Class. Quantum Grav.

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“…To find modified field equation one only needs to derive last term in action (21). In this context, the last term in action (21) given by [29] δT δg μν = T μν + T μν (22) in which T μν defined by…”

Section: Covariant Thermodynamics and New Gravity Modelmentioning

confidence: 99%

Non-conserved modified gravity theory

Fazlollahi

2023

Eur. Phys. J. C

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In the curved spacetime the conservation of stress-energy tensor $${\mathcal {T}}_{\,\,\,\,\, \mu ;\nu }^{\nu }=0$$ T μ ; ν ν = 0 has been questioned by Rastall. However, this idea in which $${\mathcal {T}}_{\,\,\,\,\, \mu ;\nu }^{\nu }=\lambda R_{,\mu }$$ T μ ; ν ν = λ R , μ is own questionable. In this study and in follows the covariant form of thermodynamics law proposed by Israel and his colleagues, the new non-conserved modified gravity is introduced. As its application, we have explored spherically symmetric solutions and evolution of the Universe for very early and late time Universe in the presence of the cosmological constant. As shown, the model gives no new result with respect to Einstein gravity for vacuum solutions, while during inflation only scalar spectra index deviates from standard model. Also, we have considered late-time and constraint model with observations through using MCMC algorithm.

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The first variation of the matter energy-momentum tensor with respect to the metric, and its implications on modified gravity theories

Cited by 2 publications

References 26 publications

A relativistic scalar model for fractional interaction between dark matter and gravity

A relativistic scalar model for fractional interaction between dark matter and gravity

Non-conserved modified gravity theory

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