广义帕拉蒂尼陈 - 西蒙斯理论中的引力波双折射
Gravitational Wave Birefringence in generalized Palatini Chern Simons
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中文总结 AI 辅助
研究与动态陈 - 西蒙斯项耦合的$f(R)$引力模型中引力波双折射现象，在度规和帕拉蒂尼形式体系下分析，考虑三种$f(R)$模型拟合数据，发现双折射增强并转换约束，且其效应随源红移呈多项式增长。
中文摘要 AI 辅助
当宇称对称性被打破时，引力波（GWs）的宇宙学传播会出现振幅和相位极化畸变，即宇宙双折射现象。本文研究了与动态陈 - 西蒙斯（dCS）项耦合的引力模型$f(R)$中GW双折射的现象学，在度规和帕拉蒂尼形式体系中进行分析。在背景水平上，该模型可导致动态暗能量，对于GW传播，帕拉蒂尼形式体系预测了振幅和速度双折射，而度规形式体系仅预测振幅双折射。$f(R)$相互作用可抑制或增强双折射效应。考虑三种常见的$f(R)$模型拟合近期宇宙学数据，发现双折射相对于$f(R)=R$的情况有所增强。还将当前GW双折射约束转换为模型中dCS耦合的界限。最后表明，在该模型中双折射效应随源红移呈多项式增长。
英文摘要
The cosmological propagation of gravitational waves (GWs) can exhibit amplitude and phase polarization distortions when parity symmetry is broken, a phenomenon known as cosmological birefringence. In this paper, we investigate the phenomenology of GW birefringence in a gravitational model $f(R)$ coupled to a dynamical Chern-Simons (dCS) term, analyzed in the metric and Palatini formalisms. At the background level, this model can lead to dynamical dark energy, while for GW propagation we find that the Palatini formalism predicts both amplitude and velocity birefringence, whereas the metric formalism predicts amplitude birefringence only. We also find that the birefringence effects can either be suppressed or enhanced by the $f(R)$ interactions, depending on the specific form of $f(R)$. Considering three common $f(R)$ models (Hu-Sawicki, Exponential, and Hyperbolic gravity) fit to recent cosmological data, we find that birefringence is enhanced relative to the $f(R) = R$ case, by $1-10\%$ in the Palatini formalism and up to a factor of 2 in the metric formalism. We also translate current GW birefringence constraints to bounds on the dCS coupling within our model. Finally, we show that in our model the birefringence effect grows polynomially with source redshift, in contrast to the linear-distance scaling commonly assumed in phenomenological models of GW birefringence in the current literature.
