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We consider a general relativistic zero-pressure irrotational cosmologicalmedium perturbed to the third order. We assume a flat Friedmann background butinclude the cosmological constant. We ignore the rotational perturbation whichdecays in expanding phase. In our previous studies we discovered that, to thesecond-order perturbation, except for the gravitational wave contributions, therelativistic equations coincide exactly with the previously known Newtonianones. Since the Newtonian second-order equations are fully nonlinear, anynonvanishing third and higher order terms in the relativistic analyses aresupposed to be pure relativistic corrections. In this work we derive suchcorrection terms appearing in the third order. Continuing our success in thesecond-order perturbations we take the comoving gauge. We discover that thethird-order correction terms are of $\phi_v$-order higher than the second-orderterms where $\phi_v$ is a gauge-invariant combination related to thethree-space curvature perturbation in the comoving gauge; compared with theNewtonian potential we have $\delta \Phi \sim {3 \over 5} \phi_v$ to the linearorder. Therefore, the pure general relativistic effects are of $varphi_v$-orderhigher than the Newtonian ones. The corrections terms are independent of thehorizon scale and depend only on the linear order gravitational potentialperturbation strength. From the temperature anisotropy of cosmic microwavebackground 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 ourprevious important practical implication that near current era one can use thelarge-scale Newtonian numerical simulation more reliably even as the simulationscale approaches near the horizon.Comment: 9 pages, no figur

Third-order perturbations of a zero-pressure cosmological medium: Pure general relativistic nonlinear effects