Tiberiu Harko
Department of Theoretical Physics, National Institute of Physics and Nuclear Engineering (IFIN-HH), Bucharest, Romania,
Department of Physics, Babes-Bolyai University, Cluj-Napoca, Romania,
School of Physics, Sun Yat-Sen University, Guan

Abstract
We investigate the coupling of matter to geometry in conformal quadratic Weyl gravity, by assuming a coupling term of the form $L_m ilde{R}^2$, where $L_m$ is the ordinary matter Lagrangian, and $ ilde{R}$ is the Weyl scalar. The coupling explicitly satisfies the conformal invariance of the theory. By expressing $ ilde{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 $fleft(R,L_m ight)$ 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 the matter Lagrangian, is generated. 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 is 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 investigated 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 $zapprox 3$.

2021 November 25, 11:00

IA/U.Lisboa
Faculdade de Ciências da Universidade de Lisboa (C8.2.03)
Campo Grande, 1749-016 Lisboa