Naonori S. Sugiyama, Toshifumi Futamase
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 unproved 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 a proof of Reg PT in the context of the standard perturbation theory, showing that Reg PT never has more effective information on the 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 the ones of Reg PT. Moreover, the 2-loop solutions in the standard perturbation theory are also better than the ones of the closure theory. This fact means that the standard perturbation theory at the 2-loop level gives the best prediction of nonlinear power spectrum at present. 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.
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http://arxiv.org/abs/1303.2748
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