论文标题
Weyl几何形状中的耦合物质和曲率：共形不变$ f \ left（r，l_m \ right）$重力
Coupling matter and curvature in Weyl geometry: conformally invariant $f\left(R,L_m\right)$ gravity
论文作者
论文摘要
我们通过假设$ l_m \ tilde {r}^2 $的耦合项来研究物质与几何形状的耦合，其中$ l_m $是普通物质的lagrangian，而$ \ tilde {r} $是weyl scalar。该耦合明确满足了该理论的形式不变性。 By expressing $\tilde{R}^2$ 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 $f\left(R,L_m\right)$ type theory, with the matter Lagrangian nonminimally coupled to the Ricci scalar.我们获得该理论的重力场方程以及能量摩托明平衡方程。物质能量量张量的差异不会消失，并且取决于Weyl载体，并产生了物质Lagrangian。还讨论了该理论的热力学解释。推导了广义的泊松方程，并详细考虑了运动方程的牛顿极限。还考虑了在存在额外力的情况下行星的圆锥体进动，并且从汞的观察数据中获得了太阳系中Weyl载体大小的约束。该理论的宇宙学含义也被考虑在平坦，均质和各向同性的Friedmann-Lemaitre-Robertson-Walker几何形状的情况下，并且表明该模型可以很好地描述Hubble功能的观察数据，直至$ z \ z \ 3 $的红shift。
We investigate the coupling of matter to geometry in conformal quadratic Weyl gravity, by assuming a coupling term of the form $L_m\tilde{R}^2$, where $L_m$ is the ordinary matter Lagrangian, and $\tilde{R}$ is the Weyl scalar. The coupling explicitly satisfies the conformal invariance of the theory. By expressing $\tilde{R}^2$ 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 $f\left(R,L_m\right)$ 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 matter Lagrangian is generated. The thermodynamic interpretation of the theory is also discussed. 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 $z\approx 3$.
