源自张量自由度的非张量引力波极化：I. 含s张量的线性化洛伦兹破缺引力理论
Nontensorial gravitational wave polarizations from the tensorial degrees of freedom: I. Linearized Lorentz-violating theory of gravity with s tensor
AI总结：
本研究在含s张量的线性化洛伦兹破缺引力理论中，证明张量自由度可直接激发非张量引力波极化，推导了该理论中引力波的传播、激发及探测特征，提出可通过多类观测约束该模型。
摘要：
广义相对论预言仅存在两种张量引力波极化，而一般的度规引力理论最多可拥有四种额外极化，包括两种矢量极化和两种标量极化。这些矢量/标量极化通常由特定引力理论的内在新增矢量/标量自由度产生。本文中我们证明，在标准模型扩展（standard model extension）的框架下，随着洛伦兹对称性的破缺，额外的非张量极化可直接由两种张量自由度激发。我们考虑引力区中具有微分同胚不变性的标准模型扩展，其包含偶质量维数d≥4的洛伦兹破缺系数$\boldsymbol{\text{ŝ}}^{(d)μρνσ}$。除了由张量模式诱导的额外极化外，该理论中的引力波传播速度依赖于传播方向，当且仅当d≥6时会发生色散，且既不存在速度双折射也不存在振幅双折射。额外极化的激发还具有手征性。此类引力波对应的干涉仪天线方向图函数通常是所有极化对应的天线方向图函数的线性组合。在该模型中，由脉冲星计时阵列（pulsar timing arrays）和盖亚（Gaia）卫星探测到的随机引力波背景，可在不同极化的光子红移与脉冲星位置的天体测量偏转的互相关之间诱导耦合。这些特性使得我们可以利用干涉仪、脉冲星计时阵列和Gaia任务来约束该模型。
英文摘要：
General relativity predicts the existence of only two tensorial gravitational wave polarizations, while a generic metric theories of gravity can possess up to four additional polarizations, including two vector and two scalar ones. These vector/scalar polarizations are in general generated by the intrinsic new vector/scalar degrees of freedom of the specific theories of gravity. In this paper, we show that, with the violation of the Lorentz symmetry in the framework of the standard model extension, the additional nontensorial polarizations can be directly excited by the two tensorial degrees of freedom. We consider the diffeomorphism invariant standard model extension in the gravity sector with the Lorentz-violating coefficients $\hat{\boldsymbol s}^{(d)μρνσ}$ of the even mass dimension $d\ge4$. In addition to the extra polarizations induced by the tensor modes, the gravitational wave in this theory travels at a speed depending on the propagation direction, experiences dispersion if and only if $d\ge6$, and possesses neither velocity nor amplitude birefringence. The excitement of the extra polarizations is also chiral. The antenna pattern functions of interferometers due to such kind of gravitational waves are generally linear combinations of those for all polarizations. Detected by pulsar timing arrays and the Gaia satellite, the stochastic gravitational wave background in this model could induce couplings among cross correlations, of the redshifts of photons and the astrometric deflections of the positions of pulsars, for different polarizations. These characteristics enable the use of interferometers, pulsar timing arrays and Gaia mission to constrain this model.
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