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arXiv 1402.0553hep-thastro-ph.COgr-qchep-ph
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具有两个暗能量和暗物质标量场的修正引力的有效场论

Effective field theory of modified gravity with two scalar fields: dark energy and dark matter

László Á. Gergely, Shinji Tsujikawa

摘要:

我们提出了一个基于两个标量自由度的讨论暗能量和暗物质宇宙学的框架。采用宇宙学扰动的有效场论。一个单一的规范选择呈现的暗能量领域的引力部门,我们采用了一个通用的拉格朗日依赖于三维几何标量产生的ADM分解。我们添加到这个暗能量相关的引力扇区的标量场$ϕ$和它的动能$X$作为暗物质变量。与单场情形相比,我们发现,为了使线性宇宙学扰动的运动方程保持在二阶,还需要满足一些附加的条件。对于这样一个二阶多场理论,我们推导出的条件下,鬼和拉普拉斯不稳定性的标量和张量扰动缺席。我们将我们的一般结果与暗能量的Horndeski理论和暗物质描述的k-本质拉格朗日$P(ϕ,X)$的框架中出现的模型。在亚视界尺度准静态近似下,我们导出了这种非流体暗物质与引力扇区之间的有效耦合。通过考虑纯动力学拉格朗日$P(X)$作为一个特殊的情况下,验证了形式主义再现引力耦合的完美流体暗物质。

英文摘要:

We present a framework for discussing the cosmology of dark energy and dark matter based on two scalar degrees of freedom. An effective field theory of cosmological perturbations is employed. A unitary gauge choice renders the dark energy field into the gravitational sector, for which we adopt a generic Lagrangian depending on three-dimensional geometrical scalar quantities arising in the ADM decomposition. We add to this dark-energy associated gravitational sector a scalar field $ϕ$ and its kinetic energy $X$ as dark matter variables. Compared to the single-field case, we find that there are additional conditions to obey in order to keep the equations of motion for linear cosmological perturbations at second order. For such a second-order multi-field theory we derive conditions under which ghosts and Laplacian instabilities of the scalar and tensor perturbations are absent. We apply our general results to models with dark energy emerging in the framework of the Horndeski theory and dark matter described by a k-essence Lagrangian $P(ϕ,X)$. We derive the effective coupling between such an imperfect-fluid dark matter and the gravitational sector under the quasi-static approximation on sub-horizon scales. By considering the purely kinetic Lagrangian $P(X)$ as a particular case, the formalism is verified to reproduce the gravitational coupling of a perfect-fluid dark matter.

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