暗能量修正引力模型中的物质密度扰动和有效引力常量
Matter density perturbations and effective gravitational constant in modified gravity models of dark energy
摘要：
对于一般拉格朗日密度f（R，φ，X），我们导出了亚视界尺度上的物质密度扰动方程，f（R，φ，X）是Ricci标量R、标量场φ和动力学项X=-（nabla φ）^2/2的函数。这对于从大尺度结构和弱透镜的观测中约束修正的引力暗能量模型是有用的。对于一些解析可解的模型，我们得到了物质微扰Δ_m和引力势φ的解。在拉格朗日密度为f（R）=alpha R^{1+m}-Lambda的f（R）暗能量模型中，扰动的增长率与标准爱因斯坦引力模型中的扰动增长率有显著差异，除非m非常接近0。在标量张量模型与拉格朗日密度f=F（φ）R+2 p（φ，X），我们与耦合的暗能量的情况下，在爱因斯坦框架的模型和重现的扰动方程已知在当前的文献中，通过保角变换。我们还估计了在约旦和爱因斯坦框架的扰动时，暗能量的能量分数是恒定的，在物质主导的时代的演变。
英文摘要：
We derive the equation of matter density perturbations on sub-horizon scales for a general Lagrangian density f(R, phi, X) that is a function of a Ricci scalar R, a scalar field phi and a kinetic term X=-(nabla phi)^2/2. This is useful to constrain modified gravity dark energy models from observations of large-scale structure and weak lensing. We obtain the solutions for the matter perturbation delta_m as well as the gravitational potential Phi for some analytically solvable models. In a f(R) dark energy model with the Lagrangian density f(R)=alpha R^{1+m}-Lambda, the growth rates of perturbations exhibit notable differences from those in the standard Einstein gravity unless m is very close to 0. In scalar-tensor models with the Lagrangian density f=F(phi)R+2p(phi,X) we relate the models with coupled dark energy scenarios in the Einstein frame and reproduce the equations of perturbations known in the current literature by making a conformal transformation. We also estimate the evolution of perturbations in both Jordan and Einstein frames when the energy fraction of dark energy is constant during the matter-dominated epoch.
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