General relativistic effects on non-linear matter power spectrum

Authors calculated the matter power spectrum based on next to the linear order perturbation theory (3rd order perturbation theory, 3PT) fully taking GR effect into account.
Basically, P_{3PT}=P_L+P_{22}+P_{13}, where non linear contributions cancel each other at large scale (P_{22}+P_{13}~0, or linear Pk is good enough), but boost up the Pk at small scale ( P_{22}+P_{13}>0).
P_{3PT} has been calculated for decades using Newtonian approximation, but this work is the first result to include genuine GR effect. As naively expected, correction due to GR is negligible, and the use of Newtonian approximation is verified.
arXiv:1010.3489