TAG Meeting-從Weyl幾何到物質與曲率的暗能量共形不變耦合

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From Weyl geometry to dark energy-conformally invariant coupling of matter and curvature

The speaker and his team investigate the coupling of matter to geometry in conformal quadratic Weyl gravity, by assuming a coupling term of the form LₘŘ², where Lₘ is the ordinary matter Lagrangian, and Ř is the Weyl scalar. The coupling explicitly satisfies the conformal invariance of the theory. By expressing Ř² 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(Ř,Lₘ) type theory, with the matter Lagrangian nonminimally coupled to the Ricci scalar. They 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 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≈3.

時間：2023.08.29(二) 19:00~20:15
地點：香港理工大學 QR513
講者：Prof. Harko
語言：英語

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