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arXiv 1707.06508astro-ph.COgr-qc
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广义Einstein-Aether模型中的宇宙学扰动理论

Cosmological perturbation theory in Generalized Einstein-Aether models

Richard A. Battye, Francesco Pace, Damien Trinh

摘要:

研究了由一般函数$\mathcal{F}(\mathcal{K})$指定的类时单位归一化矢量场描述的暗能量模型中宇宙学扰动的演化,即广义爱因斯坦-以太模型.首先,我们通过设计者的方法来研究这种模型的背景动力学,试图将这种理论建模为暗能量。我们发现,只有一个特定的形式,这种设计师的方法匹配$Λ$ CDM在背景秩序,我们也得到了一个微分方程,$\mathcal{F}(\mathcal{K})$必须满足一般$w$ CDM宇宙学。我们还提出了广义爱因斯坦-乙醚模型的扰动状态方程,它完全参数化这些模型的线性扰动水平。修改后的重力模型的一个通用特征是它们引入了新的自由度。通过完全消除这些,我们能够表示规范不变熵扰动和标量,矢量和张量各向异性应力的扰动流体变量和度量扰动。然后,这些可以用来研究标量,矢量和张量部门的扰动的演变,我们用这些来发展牛顿引力势。

英文摘要:

We investigate the evolution of cosmological perturbations in models of dark energy described by a time-like unit normalized vector field specified by a general function $\mathcal{F}(\mathcal{K})$, so-called Generalized Einstein-Aether models. First we study the background dynamics of such models via a designer approach in an attempt to model this theory as dark energy. We find that only one specific form of this designer approach matches $Λ$CDM at background order and we also obtain a differential equation which $\mathcal{F}(\mathcal{K})$ must satisfy for general $w$CDM cosmologies. We also present the equations of state for perturbations in Generalized Einstein-Aether models, which completely parametrize these models at the level of linear perturbations. A generic feature of modified gravity models is that they introduce new degrees of freedom. By fully eliminating these we are able to express the gauge invariant entropy perturbation and the scalar, vector, and tensor anisotropic stresses in terms of the perturbed fluid variables and metric perturbations only. These can then be used to study the evolution of perturbations in the scalar, vector, and tensor sectors and we use these to evolve the Newtonian gravitational potentials.

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