Distinguishing modified gravity with just two tensorial degrees of freedom from general relativity: Black holes, cosmology, and matter coupling
Distinguishing modified gravity with just two tensorial degrees of freedom from general relativity: Black holes, cosmology, and matter coupling
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DOI：
10.1103/physrevd.104.124020
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发表时间：
2021-09
影响因子：
5
通讯作者：
Aya Iyonaga;Tsutomu Kobayashi
中科院分区：
文献类型：
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作者：
Aya Iyonaga;Tsutomu Kobayashi
我们考虑空间协变修正引力，其中准标量自由度是非动力学的，因此只有两个张量自由度，即与广义相对论中相同数量的动力学自由度。围绕一类以时间的三个函数为特征的修正引力理论，我们讨论了两个张量自由度的修正引力如何从观测或现象上区别于广义相对论。经检验，该理论对弱引力场和引力波的传播速度给出了与广义相对论相同的预测。我们还发现，渐近平坦的黑洞解没有任何修改。由于理论中有很大的自由选择依赖于时间的函数，使得均匀各向同性的宇宙动力学可以接近甚至相同于$\Lambda$CDM模型的结果。我们研究了在长波长和短波长范围内的宇宙学微扰行为，结果表明，在这两个范围内，修正引力的影响只是通过修正背景演化而出现的。最后指出，在物质部分存在伽利略磁场的情况下，恢复了标量自由度，破坏了该理论的本质特征。
We consider spatially covariant modified gravity in which the would-be scalar degree of freedom is made non-dynamical and hence there are just two tensorial degrees of freedom, i.e., the same number of dynamical degrees of freedom as in general relativity. Focusing on a class of such modified gravity theories characterized by three functions of time, we discuss how modified gravity with two tensorial degrees of freedom can be distinguished observationally or phenomenologically from general relativity. It is checked that the theory gives the same predictions as general relativity for weak gravitational fields and the propagation speed of gravitational waves. We also find that there is no modification to asymptotically flat black hole solutions. Due to a large degree of freedom to choose the time-dependent functions in the theory, the homogeneous and isotropic cosmological dynamics can be made close to or even identical to that of the $\Lambda$CDM model. We investigate the behavior of cosmological perturbations in the long and short wavelength limits and show that in both limits the effects of modified gravity appear only through the modification of the background evolution. Finally, it is remarked that in the presence of a galileon field in the matter sector, the scalar degree of freedom is revived, ruining the essential feature of the theory.