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.