Cosmological implications of the Weyl geometric gravity theory

Abstract

We consider cosmological implications of the Weyl geometric gravity theory. The basic action of the model is obtained from the simplest conformally invariant gravitational action, constructed, in Weyl geometry, from the square of the Weyl scalar, the strength of the Weyl vector, and a matter term, respectively. The total action is linearized in the Weyl scalar by introducing an auxiliary scalar field. To maintain the conformal invariance of the action the trace condition is imposed on the matter energy-momentum tensor, thus making the matter sector of the action conformally invariant. The field equations are derived by varying the action with respect to the metric tensor, the Weyl vector field, and the scalar field, respectively. We investigate the cosmological implications of the theory, and we obtain first the cosmological evolution equations for a flat, homogeneous and isotropic geometry, described by Friedmann-Lemaitre-Robertson-Walker metric, which generalize the Friedmann equations of standard general relativity. In this context we consider two cosmological models, corresponding to the vacuum state, and to the presence of matter described by a linear barotropic equation of state. In both cases we perform a detailed comparison of the predictions of the theory with the cosmological observational data, and with the standard $\Lambda$ CDM model. By assuming that the presence of the Weyl geometric effects induce small perturbations in the homogeneous and isotropic cosmological background, and that the anisotropy parameter is small, the equations of the cosmological perturbations due to the presence of the Weyl geometric effects are derived. The time evolution of the metric and matter perturbations are explicitly obtained. So, if Weyl geometric effects are present, the Universe would acquire some anisotropic characteristics, and its geometry will deviate from the standard FLRW one.

22 pages, 19 figures, accepted for publication in EPJC

References in corpus (36)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• The Confrontation between General Relativity and Experiment
• f(R,T) gravity
• First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole
• First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring
• Extra force in $f(R)$ modified theories of gravity
• The trouble with $H_0$
• f(R,L_m) gravity
• The Expansion of the Universe is Faster than Expected
• Hubble parameter measurement constraints on the redshift of the deceleration-acceleration transition, dynamical dark energy, and space curvature
• $f(T,\mathcal{T})$ gravity and cosmology
• Modified theories of Gravity: Why, How and What?
• Solution to the ghost problem in fourth order derivative theories
• Cosmological observational constraints on the power law $f(Q)$ type modified gravity theory
• Quasinormal modes of black holes in f(T) gravity
• Black hole solutions in the quadratic Weyl conformal geometric theory of gravity
• Dark matter as a Weyl geometric effect
• Non-metric geometry as the origin of mass in gauge theories of scale invariance
• Palatini formulation of the conformally invariant $f\left(R,L_m\right)$ gravity theory
• On the proper kinetic quadrupole CMB removal and the quadrupole anomalies
• Coupling matter and curvature in Weyl geometry: conformally invariant $f\left(R,L_m\right)$ gravity
• A Weyl-Dirac Cosmological Model with DM and DE
• Constraining $f(T,\mathcal{T})$ Gravity with Gravitational Baryogenesis
• Anisotropic Weyl symmetry and cosmology
• Compact stellar structures in Weyl geometric gravity
• Curvature-matter couplings in modified gravity: from linear models to conformally invariant theories
• Growth of structures using redshift space distortion in $f(T)$ Cosmology
• Compact stars in $f(T)=T+\xi T^{\beta }$ gravity
• $f(T)$ cosmology in the regime of quasar observations
• Quantum scale invariance in gauge theories and applications to muon production
• Renormalization Group for Non-minimal ${\varphi }^{2}R$ Couplings and Gravitational Contact Interactions
• Torsional Weyl-Dirac Electrodinamics
• Weyl cosmology
• Cosmological particle creation in Weyl geometry
• Supervisor of the Universe

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• On Scalar Cosmological Perturbations in Non-Minimally Coupled Weyl Connection Gravity
• Inflation in light of ACT/SPT: A new perspective from Weyl gravity
• Cosmological test of a length-preserving biconnection gravity
• The Weyl Geometric Gravity black hole in light of the Solar System tests