On the necessity of the revisions for the cosmological matter
  perturbations from the general relativity
  The differential equations, which are used for matter perturbations, are
usually derived from the Newton gravity and the Euler equation in the expanded
universe. In this paper, by the explicit calculations of metric perturbation
theory in $\Lambda$CDM model, we derive the general relativistic corrections
exactly for the equations and show that the differential equations derived from
the Newton gravity and the Euler equation are valid in the small scale region
from non-relativistic matter dominant era onwards. However the corrections are
not negligible in radiation dominant era.
