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arXiv 2002.03676gr-qchep-th
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两个小的四阶导数修正下引力场中宇宙暴胀的引力波

Gravitational wave from cosmic inflation in a gravity with two small four-derivative corrections

Chae-min Yun

摘要:

我们研究了一个暴胀宇宙学模型,其中最小耦合标量场理论被附加的修正项所修正。在Weinberg在有效场论背景下提出的最一般的十个修正项中,我们仅考虑两个项:$f_1(ϕ) R^2$和$f_2(ϕ) R^{ab}R_{ab}$,遵循Noh和Hwang的工作,其中$f_1$和$f_2$是常数。由此模型导出了背景宇宙和张量型微扰的四阶微分方程。我们表明,这些方程可以减少到二阶方程,假设$f_n$是小的。由这些近似方程,我们发现由于$f_2$项的存在,引力波的传播速度略小于光速,并且张量型扰动的演化在大尺度极限下是守恒的.

英文摘要:

We investigate a model of inflationary cosmology where the minimally coupled scalar field theory is modified by additional correction terms. Among the most general ten correction terms remarked by Weinberg in context of effective field theory, we consider only two terms, $f_1(ϕ) R^2$ and $f_2(ϕ) R^{ab}R_{ab}$, following the work by Noh and Hwang where $f_1$ and $f_2$ are constant. The fourth order differential equations for the background universe and the tensor-type perturbation are derived out of this model. We show that these equations can be reduced to second order equations, supposing that $f_n$ are small. From these approximated equations, we find that the propagation speed of gravitational wave is slightly less than the speed of light due to $f_2$ term, and that the evolution of the tensor-type perturbation is conserved in the large scale limit.

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