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arXiv 1201.4630gr-qcastro-ph.COhep-th
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广义协变引力理论中的暴胀

Inflation in general covariant theory of gravity

Yongqing Huang, Anzhong Wang, Qiang Wu

摘要:

本文在具有可投射性条件和任意耦合常数$λ$的Hoenava-Lifshitz引力的非相对论性广义协变理论框架下研究暴胀问题.我们发现,Friedmann-Robterson-Walker(FRW)宇宙在这样的设置必然是平坦的。我们在不指定特定规范的情况下,明确地计算了平坦FRW宇宙的线性微扰,发现由于高阶空间导数项的存在,微扰不同于广义相对论中的微扰.将一般公式应用于单个标量场,我们证明了在亚视界区域,度规场和标量场是紧耦合的,并且具有相同的振荡频率。在超视界区,扰动变为绝热的,共动曲率扰动为常数。我们还计算了标量和张量扰动的功率谱和指数,并将它们明确地表示为慢滚参数和高阶空间导数项的耦合常数。特别地,我们发现标量和张量的扰动几乎是尺度不变的,并且谱指数与GR中给出的相同,但是标量和张量功率谱的比值取决于高阶空间导数项,并且可以与GR中的显著不同.

英文摘要:

In this paper, we study inflation in the framework of the nonrelativistic general covariant theory of the Hořava-Lifshitz gravity with the projectability condition and an arbitrary coupling constant $λ$. We find that the Friedmann-Robterson-Walker (FRW) universe is necessarily flat in such a setup. We work out explicitly the linear perturbations of the flat FRW universe without specifying to a particular gauge, and find that the perturbations are different from those obtained in general relativity, because of the presence of the high-order spatial derivative terms. Applied the general formulas to a single scalar field, we show that in the sub-horizon regions, the metric and scalar field are tightly coupled and have the same oscillating frequencies. In the super-horizon regions, the perturbations become adiabatic, and the comoving curvature perturbation is constant. We also calculate the power spectra and indices of both the scalar and tensor perturbations, and express them explicitly in terms of the slow roll parameters and the coupling constants of the high-order spatial derivative terms. In particular, we find that the perturbations, of both scalar and tensor, are almost scale-invariant, and the spectrum indices are the same as those given in GR, but the ratio of the scalar and tensor power spectra depends on the high-order spatial derivative terms, and can be different from that of GR significantly.

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