Nonminimally coupled Weyl gravity

Gomes, Cláudio; Bertolami, Orfeu

doi:10.1088/1361-6382/ab52b9

“…Recently, the Weyl gravity has been revived to solve the dark matter and dark energy problems or inflation [28]. Gomes et al [29] investigated the non-minimal coupling between the curvature and matter in the Weyl gravity theory. In the framework of proper Weyl geometry, Yixin et al [30] introduced a non-minimal coupling between nonmetricity Q and the trace of energy-momentum tensor, where the non-metricity is completely determined by the magnitude of the vector field ω μ .…”

Section: Introductionmentioning

confidence: 99%

Viscous cosmology in the Weyl-type f(Q, T) gravity

Gadbail

¹

,

Arora

²

,

Sahoo

³

2021

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Bulk viscosity is the only viscous influence that can change the background dynamics in a homogeneous and isotropic universe. In the present work, we analyze the bulk viscous cosmological model with the bulk viscosity coefficient of the form $$\zeta =\zeta _0+\zeta _1H+\zeta _2\left( \frac{\dot{H}}{H}+H\right) $$ ζ = ζ 0 + ζ 1 H + ζ 2 H ˙ H + H where, $$\zeta _0$$ ζ 0 , $$\zeta _1$$ ζ 1 and $$\zeta _2$$ ζ 2 are bulk viscous parameters, and H is the Hubble parameter. We investigate the impact of the bulk viscous parameter on dynamics of the universe in the recently proposed Weyl-type f(Q, T) gravity, where Q is the non-metricity, and T is the trace of the matter energy–momentum tensor. The exact solutions to the corresponding field equations are obtained with the viscous fluid and the linear model of the form $$f(Q, T)=\alpha Q+\frac{\beta }{6\kappa ^2}T$$ f ( Q , T ) = α Q + β 6 κ 2 T , where $$\alpha $$ α and $$\beta $$ β are model parameters. Further, we constrain the model parameters using the 57 points Hubble dataset the recently released 1048 points Pantheon sample and the combination Hz + BAO + Pantheon, which shows our model is good congeniality with observations. We study the possible scenarios and the evolution of the universe through the deceleration parameter, the equation of state (EoS) parameter, the statefinder diagnostics, and the Om diagnostics. It is observed that the universe exhibits a transition from a decelerated to an accelerated phase of the universe under certain constraints of model parameters.

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“…This is a relevant result since the difference between the theory studied in this work and the one from Ref. [7] is the existence of dynamics of the Weyl field. Hence, the introduction of this dynamical term in the Lagrangian of the theory induces a constraint on the field which limits the number of consistent effective theories that are free from Ostrogradsky instabilities.…”

Section: Resultsmentioning

confidence: 63%

“…The resulting theory, dubbed as non-minimally coupled Weyl connection gravity (NMCWCG) has been previously studied in Refs. [7,8]. This paper follows the work done in previous references and focuses on the Hamiltonian of the NMCWCG theories and on searching instabilities, particularly Ostrogradsky instabilities.…”

Section: Introductionmentioning

confidence: 96%

Cosmological solutions of the non-minimally coupled Weyl connection gravity theories

Baptista¹,

Bertolami²

2020

Class. Quantum Grav.

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We study the Hamiltonian formalism of the non-minimally coupled Weyl connection gravity (NMCWCG) in order to check whether Ostrogradsky instabilities are present. The Hamiltonian of the NMCWCG theories is obtained by foliating space-time into a real line (representing time) and 3-dimensional space-like hypersurfaces, and by considering the spatial metric and the extrinsic curvature of the hypersurfaces as the canonical coordinates of the theory. Given the fact that the theory we study contains an additional dynamical vector field compared to the usual NMC models, which do not have Ostrogradsky instabilities, we are able to construct an effective theory without these instabilities, by constraining this Weyl field.

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“…In the context of f (Q)-gravity, it has been recently proposed [66] a coupling with matter that deserves an immediate analysis due to the appearance of an extra force in the geodesic equation (with the Levi-Civita connection). And more recently, the case of a non-minimal coupling between matter and geometry in manifolds endowed with a non-metric connection has gained growing attention [67][68][69]. Thus, the issue of whether generalized proper time can be regarded as physical might depend on the particular model, since the possibility of constructing a generalized clock within every model depends on its particular geometry-matter coupling.…”

Section: Discussionmentioning

confidence: 99%

Conformally invariant proper time with general non-metricity

Delhom

¹

,

Lobo

²

,

Olmo

³

et al. 2020

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We show that the definition of proper time for Weyl-invariant space-times given by Perlick naturally extends to spaces with arbitrary non-metricity. We then discuss the relation between this generalized proper time and the Ehlers-Pirani-Schild definition of time when there is arbitrary non-metricity. Then we show how this generalized proper time suffers from a second clock effect. Assuming that muons are a device to measure this proper time, we constrain the non-metricity tensor on Earth's surface and then elaborate on the feasibility of such assumption.

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Nonminimally coupled Weyl gravity

Abstract: Weyl gravity in the presence of a non-minimal matter-curvature coupling is presented. Some properties arising from the non-metricity give rise to a second order theory whose vacuum is compatible with a cosmological constant, under conditions on the vector field.

Cited by 9 publications

References 92 publications

Viscous cosmology in the Weyl-type f(Q, T) gravity

Viscous cosmology in the Weyl-type f(Q, T) gravity

Cosmological solutions of the non-minimally coupled Weyl connection gravity theories

Conformally invariant proper time with general non-metricity

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