Relation between standard perturbation theory and regularized
  multi-point propagator method
  We investigate the relation between the regularized multi-propagator method,
called "Reg PT", and the standard perturbation theory. Reg PT is one of the
most successful models to describe nonlinear evolution of dark matter
fluctuations. However, Reg PT is a mathematically unproven interpolation
formula between the large-scale solution calculated by the standard
perturbation theory and the limiting solution in the small scale calculated by
the multi-point propagator method. In this paper, we give an alternative
explanation for Reg PT in the context of the standard perturbation theory,
showing that Reg PT does not ever have more effective information on nonlinear
matter evolution than the standard perturbation theory. In other words, the
solutions of the standard perturbation theory reproduce the results of $N$-body
simulations better than those of Reg PT, especially at the high-$k$ region.
This fact means that the standard perturbation theory at the two-loop level is
still one of the best predictions of the nonlinear power spectrum to date.
Nevertheless, the standard perturbation theory has not been preferred because
of the divergent behavior of the solution at small scales. To solve this
problem, we also propose a modified standard perturbation theory which avoids
the divergence.
