http://arxiv.org/abs/1505.03323
$f(R)$ gravity is one of the simplest theories of modified gravity to explain the accelerated cosmic expansion. Although it is usually assumed that the quasi-Newtonian approach for cosmic perturbations is good enough to describe the evolution of large scale structure in $f(R)$ models, some studies have suggested that this method is not valid for all $f(R)$ models. Here, we show that in the matter-dominated era, the pressure and shear equations alone, which can be recast into four first-order equations to solve for cosmological perturbations exactly, are sufficient to solve for the Newtonian potential, $\Psi$, and the curvature potential, $\Phi$. Based on these two equations, we are able to clarify how the exact linear perturbations fit into different limits. We find that in the subhorizon limit, the so called quasi-static assumption plays no role in reducing the exact linear perturbations in any viable $f(R)$ gravity. Our findings also disagree with previous studies where we find little difference between our exact solutions and that of the quasi-Newtonian approach even up to $k=10 c^{-1} H_0$.
M. Chiu, A. Taylor, C. Shu, et. al.
Thu, 14 May 15
8/57
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