论文标题
标量调整的暗能量与暗物质中的宇宙学扰动的一般表述
General formulation of cosmological perturbations in scalar-tensor dark energy coupled to dark matter
论文作者
论文摘要
对于标量字段$ ϕ $耦合到冷暗物质（CDM），我们提供了一个一般框架，用于研究各向同性宇宙学背景的背景和扰动动力学。黑暗能源部门用Horndeski Lagrangian描述，其引力速度相当于光的速度，而CDM则以数字密度$ n_c $和四速度$ u_c^μ$为特征的完美流体。 For a very general interacting Lagrangian $f(n_c, ϕ, X, Z)$, where $f$ depends on $n_c$, $ϕ$, $X=-\partial^μ ϕ\partial_μ ϕ/2$, and $Z=u_c^μ \partial_μ ϕ$, we derive the full linear perturbation equations of motion without fixing any gauge conditions.为了实现成功结构形成的消失的CDM音速，相互作用的函数需要为$ f = -f_1（ϕ，x，z）n_c+f_2（ϕ，x，x，z）$的形式。在声音范围内深处的模式中采用准静态近似，我们获得了CDM和Baryon密度扰动的有效重力耦合以及重力和弱透镜电位的分析公式。我们将通用公式应用于几种相互作用的理论，并表明，在许多情况下，由于$ f_2 $ $ z $依赖性引起的动量转移，因此，围绕准de-de-de-de-de-de-sitter背景的CDM重力耦合可能小于牛顿常数$ g $。
For a scalar field $ϕ$ coupled to cold dark matter (CDM), we provide a general framework for studying the background and perturbation dynamics on the isotropic cosmological background. The dark energy sector is described by a Horndeski Lagrangian with the speed of gravitational waves equivalent to that of light, whereas CDM is dealt as a perfect fluid characterized by the number density $n_c$ and four-velocity $u_c^μ$. For a very general interacting Lagrangian $f(n_c, ϕ, X, Z)$, where $f$ depends on $n_c$, $ϕ$, $X=-\partial^μ ϕ\partial_μ ϕ/2$, and $Z=u_c^μ \partial_μ ϕ$, we derive the full linear perturbation equations of motion without fixing any gauge conditions. To realize a vanishing CDM sound speed for the successful structure formation, the interacting function needs to be of the form $f=-f_1(ϕ, X, Z)n_c+f_2(ϕ, X, Z)$. Employing a quasi-static approximation for the modes deep inside the sound horizon, we obtain analytic formulas for the effective gravitational couplings of CDM and baryon density perturbations as well as gravitational and weak lensing potentials. We apply our general formulas to several interacting theories and show that, in many cases, the CDM gravitational coupling around the quasi de-Sitter background can be smaller than the Newton constant $G$ due to a momentum transfer induced by the $Z$-dependence in $f_2$.
