Model of a spin-$1/2$ electric charge in $F\left( B^2\right)$ modified Weyl gravity

Is Asymptotically Weyl-Invariant Gravity Viable?

We explore the cosmological viability of a theory of gravity defined by the Lagrangian $f(\mathcal{R})=\mathcal{R}^{n\left(\mathcal{R}\right)}$ in the Palatini formalism, where $n\left(\mathcal{R}\right)$ is a dimensionless function of the Palatini scalar curvature $\mathcal{R}$ that interpolates between general relativity when $n\left(\mathcal{R}\right)=1$ and a locally scale-invariant and superficially renormalizable theory when $n\left(\mathcal{R}\right)=2$. We refer to this model as asymptotically Weyl-invariant gravity (AWIG). We analyse perhaps the simplest possible implementation of AWI…

Coupling matter and curvature in Weyl geometry: conformally invariant $f\left(R,L_m\right)$ gravity

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.…

Spinor field solutions in $F\left(B^2\right)$ modified Weyl gravity

We consider modified Weyl gravity where a Dirac spinor field is nonminimally coupled to gravity. It is assumed that such modified gravity is some approximation for the description of quantum gravitational effects related to the gravitating spinor field. It is shown that such a theory contains solutions for a class of metrics which are conformally equivalent to the Hopf metric on the Hopf fibration. For this case, we obtain a full discrete spectrum of the solutions and show that they can be related to the Hopf invariant on the Hopf fibration. The expression for the spin operator in the Hopf coo…

平面对称时空中的 Weyl 中微子

Weyl Neutrinos In Plane Symmetric Spacetimes

该研究在复四元数框架下推导耦合 Einstein–Weyl 方程，并构造描述左行与右行中微子平面波的两族平面对称精确解。

射影曲率张量在 $f\left(R,G\right)$、$f\left(R,T\right)$ 与 $f\left(R,L_{m}\right)$ 引力中的影响

Impact of projective curvature tensor in $f\left(R,G\right)$, $f\left(R,T\right)$ and $f\left(R,L_{m}\right)$-gravity

本文利用射影曲率张量刻画 $f(R,G)$、$f(R,T)$ 和 $f(R,L_m)$ 引力中的完美流体时空，证明射影平坦情形对应暗能量时代，并借助 $f(R,G)=\exp(R)+α(6G)^β$ 模型验证能量条件与宇宙加速膨胀一致。