arXiv subjects

Yu-Zhi Fan

Publications and source records attributed to Yu-Zhi Fan.

6 recordsLinked to original sources

arXiv2026

Gravitational wave polarization modes and stability analysis in Weyl geometry gravity

We investigate the gravitational wave polarization modes and stability in Weyl geometry gravity within a Minkowski background. Our results indicate that the tensor sector consists of two standard modes propagating at the speed of light. Although the vector sector possesses a dynamical degree of freedom, it generates no polarization modes. The scalar sector, in contrast, features a mixture mode of breathing and longitudinal modes associated with a single scalar degree of freedom. This degree of freedom exhibits superluminal propagation and intrinsic amplitude decay, both driven by the background Weyl gauge field. We further discuss the observational detectability of this scalar mode. Our stability analysis reveals that, while the tensor and vector sectors are free from ghost and Laplacian instabilities, the scalar sector suffers from an Ostrogradsky ghost instability. These findings clarify the unique gravitational wave propagation characteristics in Weyl geometry gravity and provide theoretical foundations for testing the theory through future multi-messenger observations.

gr-qc↗

arXiv2026

Cosmological perturbations and gravitational waves in the general Einstein-vector theory

We investigate the stability and gravitational waves (GWs) in the four-dimensional general Einstein-vector theory on a cosmological background. To study the stability, we systematically perform a Hamiltonian analysis at the linear perturbation level. The stability conditions are easily satisfied for tensor perturbations, but they impose nontrivial constraints on the parameter space for vector and scalar perturbations. In particular, in the presence of a nonzero background vector field, the scalar sector fails to satisfy the stability conditions in the general parameter space. However, imposing the plane-wave condition relaxes these conditions, making them achievable. In the small-scale limit, we further investigate the GW properties of the general Einstein-vector theory within the stable parameter space, including the number of independent modes, their propagation speeds, and observational constraints from GW experiments. We find that there can be at most two tensor modes, two vector modes, and one scalar mode. Notably, without imposing the plane-wave ansatz, no scalar GWs exist within the stable parameter space. Furthermore, vector GWs are forbidden if tensor GWs propagate exactly at the speed of light.

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arXiv2025

Stability Analysis of Cosmological Perturbations in the Bumblebee Model: Parameter Constraints and Gravitational Waves

We constrain the parameter space of the Bumblebee model in a cosmological background and then investigate the properties of gravitational waves within the constrained parameter space. Our analysis reveals seven perturbative degrees of freedom in the cosmological background: two tensor, two vector, and two scalar modes, along with an additional mode from the matter sector. The stability conditions for all these modes are derived. By incorporating the observed accelerated expansion of the universe and the observational constraints on tensor gravitational waves, we derive bounds on the parameter space of the Bumblebee model. Our results indicate that the non-minimal coupling parameter $\xi$ must be non-positive, a constant background value $b_{t}$ of the Bumblebee field implies $\sigma\ne -\tfrac{1}{2}\xi$, and the Lorentz-violating parameter $\xi b^2$ has a lower bound on the order of $10^{-15}$. We then investigate the propagation characteristics and polarization modes of gravitational waves in both the small-scale and Minkowski limits. The propagation modes of gravitational waves in the Bumblebee model consist of two tensor modes, two vector modes, and one scalar mode. Notably, the tensor modes travel at subluminal speeds, whereas the vector and scalar modes propagate at superluminal speeds, when $\xi b_{t}^2\ne 0$. These results provide a concrete theoretical framework and specific observational signatures for testing Lorentz invariance in the gravitational sector with future gravitational-wave detectors.

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arXiv2025

Polarization modes of gravitational waves in general symmetric teleparallel gravity

In this paper, we investigate the polarization modes of gravitational waves within the most general symmetric teleparallel gravity theory that allows for second-order field equations We consider both scenarios where test particles either carry or do not carry a hypermomentum charge. Our findings reveal the existence of tensor, vector, and scalar modes of gravitational waves. Firstly, the theory supports the + and $\times$ tensor modes propagating at the speed of light. Secondly, in the case where particles do not carry hypermomentum, vector modes propagating at the speed of light exist only within a very specific parameter space. However, when particles do carry hypermomentum, there are two shear modes that propagate at the speed of light, while the vector-$x$ and vector-$y$ modes emerge only under very specific conditions. Thirdly, in the presence of hypermomentum, there is always a longitudinal mode propagating at the speed of light. The universal existence of the shear modes and the longitudinal mode in the presence of hypermomentum is a key feature of symmetric teleparallel gravity, distinguishing it from the Riemannian framework through gravitational wave polarization detection. We also analyze the polarization modes in two widely studied special theories: $f(Q)$ theory and quadratic non-metricity theory. Our study reveals that, within the $f(Q)$ gravity framework, it is crucial to assume that matter fields are independent of the connection, as any dependence would lead to unphysical results.

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arXiv2025

New gravitational wave polarization modes in the torsionless spacetime

In this study, we investigate the polarization properties of gravitational waves within a torsionless spacetime framework, as described by the Palatini formalism. Our analysis uncovers the presence of two novel polarization modes, referred to as shear modes, which extend beyond the traditional set of six modes in a four-dimensional Riemannian spacetime. These shear modes, uniquely driven by vector degrees of freedom associated with non-metricity, are classified as vector modes, and their detection provides a unique opportunity to explore the fundamental structure of spacetime and to test gravity theories. These modes extend the standard gravitational wave polarization paradigm and provide novel observational signatures for gravitational wave detectors.

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arXiv2024

Polarization modes of gravitational waves in scalar-tensor-Rastall theory

Rastall theory, originally introduced in 1972, suggests a violation of the usual conservation law. We consider two generalizations of Rastall theory: Brans-Dicke-Rastall theory and the newly established scalar-tensor-Rastall theory, the latter being a further generalization of the former. The field equations in these two generalized theories are studied across different parameter spaces, and the polarization modes of gravitational waves, as a key focus, are subsequently investigated. The results show that the polarization modes of gravitational waves in Brans-Dicke-Rastall theory are the same as those in Brans-Dicke theory; specifically, both theories exhibit the plus, cross, and breathing modes. However, in scalar-tensor-Rastall theory, the polarization modes of gravitational waves depend on the parameter space of the theory. Particularly, over a broad range of the parameter space, regardless of some special values of the parameters, it allows only two tensor modes, just as in general relativity, without introducing any additional degrees of freedom. This indicates that Rastall theory offers a novel approach to constructing modified gravity theories that propagate only two tensor degrees of freedom. In the remaining regions of the parameter space, there is also one scalar mode in addition to the two tensor modes. The scalar mode can be either a mixture of the breathing and longitudinal modes or just a pure breathing mode, depending on the parameter space. These results will play a crucial role in constraining the theoretical parameters through future gravitational wave detection projects, such as LISA, Taiji, and TianQin.

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