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The Early-Time Evolution of the Cosmological Perturbations in f(R) Gravity

We investigate the evolution of the linear cosmological perturbations in f(R) gravity, an alternative to dark energy for explaining the late-time cosmic acceleration. We numerically calculate the early-time evolution with an approximation we contrive to solve a problem that commonly appears when one solves the full evolution equations. With the approximate evolution equations we can fairly assess the effect of the gravity modification on the early-time evolution, thereby examining the validity of the general-relativity (GR) approximation that is widely used for the early universe. In particular, we compare the CMB photon density perturbation and the matter density perturbation obtained respectively by our approximation and the conventional GR approximation. We find that the effect of the gravity modification at early times in f(R) gravity may not be negligible. We conclude that to be self-consistent, in the f(R) theory one should employ the approximation presented in this paper instead of that of GR in the treatment of the early-time evolution.