  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.
