  We consider a general relativistic zero-pressure irrotational cosmological
medium perturbed to the third order. We assume a flat Friedmann background but
include the cosmological constant. We ignore the rotational perturbation which
decays in expanding phase. In our previous studies we discovered that, to the
second-order perturbation, except for the gravitational wave contributions, the
relativistic equations coincide exactly with the previously known Newtonian
ones. Since the Newtonian second-order equations are fully nonlinear, any
nonvanishing third and higher order terms in the relativistic analyses are
supposed to be pure relativistic corrections. In this work we derive such
correction terms appearing in the third order. Continuing our success in the
second-order perturbations we take the comoving gauge. We discover that the
third-order correction terms are of $\phi_v$-order higher than the second-order
terms where $\phi_v$ is a gauge-invariant combination related to the
three-space curvature perturbation in the comoving gauge; compared with the
Newtonian potential we have $\delta \Phi \sim {3 \over 5} \phi_v$ to the linear
order. Therefore, the pure general relativistic effects are of $varphi_v$-order
higher than the Newtonian ones. The corrections terms are independent of the
horizon scale and depend only on the linear order gravitational potential
perturbation strength. From the temperature anisotropy of cosmic microwave
background we have ${\delta T \over T} \sim {1 \over 3} \delta \Phi \sim {1
\over 5} \phi_v \sim 10^{-5}$. Therefore, our present result reinforces our
previous important practical implication that near current era one can use the
large-scale Newtonian numerical simulation more reliably even as the simulation
scale approaches near the horizon.
