Cosmology in generalized Horndeski theories with second-order equations of motion
Cosmology in generalized Horndeski theories with second-order equations of motion
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DOI：
10.1103/physrevd.90.044073
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发表时间：
2014-07
影响因子：
5
通讯作者：
R. Kase;S. Tsujikawa
中科院分区：
文献类型：
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作者：
R. Kase;S. Tsujikawa
本文研究了在平坦的Friedmann-Lema\^{i}tre-Robertson-步行者（FLRW）背景下的Horndeski理论的扩展版本的二阶运动方程的宇宙学.除了与引力扇区相关的暗能量场$\chi$之外，我们还考虑了多个标量场$\phi_I$（$I= 1，2\cdots，N-1$），这些标量场由拉格朗日量$P^{（I）}（X_I）$表征，其中$X_I=\partial_{\mu}\phi_I\partial^{\mu}\phi_I$。这些额外的标量场可以模拟辐射和非相对论物质的完美流体。我们推导出标量和张量扰动的传播速度以及鬼的情况下的条件。超越Horndeski的理论诱导非平凡的修改所有的传播速度的$N$标量场，但修改的物质场$\phi_I$一般被抑制相对于暗能量场$\chi$。我们应用我们的结果，协变Galileon与爱因斯坦-希尔伯特项，其中的Minkowski Galileon的偏导数被替换为协变导数。与一般时空中二阶运动方程的协变伽利略理论不同，对于晚期追踪解，与场$\chi$相关的标量传播速度平方$c_{s1}^2$在物质时代变为负值，因此两个伽利略理论可以在线性宇宙学微扰的水平上清楚地区分开来。
We study the cosmology of an extended version of Horndeski theories with second-order equations of motion on the flat Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) background. In addition to a dark energy field $\chi$ associated with the gravitational sector, we take into account multiple scalar fields $\phi_I$ ($I=1,2\cdots,N-1$) characterized by the Lagrangians $P^{(I)}(X_I)$ with $X_I=\partial_{\mu}\phi_I\partial^{\mu}\phi_I$. These additional scalar fields can model the perfect fluids of radiation and non-relativistic matter. We derive propagation speeds of scalar and tensor perturbations as well as conditions for the absence of ghosts. The theories beyond Horndeski induce non-trivial modifications to all the propagation speeds of $N$ scalar fields, but the modifications to those for the matter fields $\phi_I$ are generally suppressed relative to that for the dark energy field $\chi$. We apply our results to the covariantized Galileon with an Einstein-Hilbert term in which partial derivatives of the Minkowski Galileon are replaced by covariant derivatives. Unlike the covariant Galileon with second-order equations of motion in general space-time, the scalar propagation speed square $c_{s1}^2$ associated with the field $\chi$ becomes negative during the matter era for late-time tracking solutions, so the two Galileon theories can be clearly distinguished at the level of linear cosmological perturbations.