Perturbation theory challenge for cosmological parameters estimation:
  Matter power spectrum in real space
  We study the accuracy with which cosmological parameters can be determined
from real space power spectrum of matter density contrast at weakly nonlinear
scales using analytical approaches. From power spectra measured in $N$-body
simulations and using Markov chain Monte-Carlo technique, the best-fitting
cosmological input parameters are determined with several analytical methods as
a theoretical template, such as the standard perturbation theory, the
regularized perturbation theory, and the effective field theory. We show that
at redshift 1, all two-loop level calculations can fit the measured power
spectrum down to scales $k \sim 0.2 \, h \, \mathrm{Mpc}^{-1}$ and cosmological
parameters are successfully estimated in an unbiased way. Introducing the
Figure of bias (FoB) and Figure of merit (FoM) parameter, we determine the
validity range of those models and then evaluate their relative performances.
With one free parameter, namely the damping scale, the regularized perturbation
theory is found to be able to provide the largest FoM parameter while keeping
the FoB in the acceptance range.
