arXiv 2005.084282020-05gr-qcastro-ph.COhep-th

相容$D\to 4$ Einstein-Gauss-Bonnet引力中的宇宙学和引力波

Cosmology and gravitational waves in consistent $D\to 4$ Einstein-Gauss-Bonnet gravity

Katsuki Aoki, Mohammad Ali Gorji, Shinji Mukohyama

备注：: 18 pages, no figures, new subsection added, accepted for publication in JCAP, observational constraints corrected

摘要：

在最近的一篇文章[1]中，我们提出了一个新的具有两个动力学自由度的$4$维引力理论，它是具有重新标度的Gauss-Bonnet耦合常数$\tildeα$的$D\to4$ Einstein-Gauss-Bonnet引力的一致实现。这是通过打破一部分非同态不变性而实现的，因此与洛夫洛克定理一致。在本文中，我们研究宇宙学的理论在一个完美的流体的存在下，并澄清从一致的$4$维理论和以前认为，天真（和不一致）的$D\rightarrow 4$限制的结果之间的相似性和差异。通过对线性扰动的研究，我们明确地证明了该理论只有张量引力自由度（除了物质自由度之外），并且对于$\tildeα>0$和$\dot{H}<0$，扰动没有任何病态，这样我们就可以实现建立早期和/或晚期宇宙学模型的设置.有趣的是，$k^4$项出现在张量模的色散关系中，它在小尺度下起着重要的作用，使该理论不仅不同于广义相对论，也不同于许多其他修正的引力理论以及天真（和不一致）的$D\to 4$极限。考虑到$k^4$项，观测对引力波传播的约束产生了约束$\tildeα \lesssim (10\,{\rm meV})^{-2}$。这是$D\to 4$ Einstein-Gauss-Bonnet引力相容理论中唯一参数（除了牛顿常数和源于时间规范固定的约束选择）的第一个界限。

英文摘要：

In a very recent paper [1], we have proposed a novel $4$-dimensional gravitational theory with two dynamical degrees of freedom, which serves as a consistent realization of $D\to4$ Einstein-Gauss-Bonnet gravity with the rescaled Gauss-Bonnet coupling constant $\tildeα$. This has been made possible by breaking a part of diffeomorphism invariance, and thus is consistent with the Lovelock theorem. In the present paper, we study cosmological implications of the theory in the presence of a perfect fluid and clarify the similarities and differences between the results obtained from the consistent $4$-dimensional theory and those from the previously considered, naive (and inconsistent) $D\rightarrow 4$ limit. Studying the linear perturbations, we explicitly show that the theory only has tensorial gravitational degrees of freedom (besides the matter degree) and that for $\tildeα>0$ and $\dot{H}<0$, perturbations are free of any pathologies so that we can implement the setup to construct early and/or late time cosmological models. Interestingly, a $k^4$ term appears in the dispersion relation of tensor modes which plays significant roles at small scales and makes the theory different than not only general relativity but also many other modified gravity theories as well as the naive (and inconsistent) $D\to 4$ limit. Taking into account the $k^4$ term, the observational constraint on the propagation of gravitational waves yields the bound $\tildeα \lesssim (10\,{\rm meV})^{-2}$. This is the first bound on the only parameter (besides the Newton's constant and the choice of a constraint that stems from a temporal gauge fixing) in the consistent theory of $D\to 4$ Einstein-Gauss-Bonnet gravity.

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英文摘要：

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