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arXiv 1506.04543hep-thastro-ph.COgr-qc
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双引力理论中早期宇宙的稳定性

Stability of the Early Universe in Bigravity Theory

Katsuki Aoki, Kei-ichi Maeda, Ryo Namba

摘要:

在无重影的双引力理论中,我们研究了平坦Friedmann-Lema $\hatı$ tre-Robertson-Walker时空周围球对称扰动的稳定性,保留了大质量引力子螺旋度- $0$模的非线性.当引力子的质量小于哈勃参数时,均匀各向同性时空在双引力场的线性扰动下会出现Higuchi型鬼现象或梯度不稳定性。因此,双引力理论在线性水平上的宇宙学解没有健康的无质量极限。在本文中,我们证明了在适当的耦合常数参数空间中,考虑标量引力子模的非线性效应,可以解决不稳定性问题。双引力中的增长历史可以恢复到宇宙早期阶段的广义相对论的结果,此时Stückelberg场是非线性的,既没有鬼场,也没有梯度不稳定性。因此,双引力理论具有健康的无质量极限,即使引力子质量小于哈勃参数,基于它的宇宙学也是可行的。

英文摘要:

We study the stability of a spherically symmetric perturbation around the flat Friedmann-Lema$\hatı$tre-Robertson-Walker spacetime in the ghost-free bigravity theory, retaining nonlinearities of the helicity-$0$ mode of the massive graviton. It has been known that, when the graviton mass is smaller than the Hubble parameter, homogeneous and isotropic spacetimes suffer from the Higuchi-type ghost or the gradient instability against the linear perturbation in the bigravity. Hence, the bigravity theory has no healthy massless limit for cosmological solutions at linear level. In this paper we show that the instabilities can be resolved by taking into account nonlinear effects of the scalar graviton mode for an appropriate parameter space of coupling constants. The growth history in the bigravity can be restored to the result in general relativity in the early stage of the Universe, in which the Stückelberg fields are nonlinear and there is neither ghost nor gradient instability. Therefore, the bigravity theory has the healthy massless limit, and cosmology based on it is viable even when the graviton mass is smaller than the Hubble parameter.

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