Perturbation Theory Remixed: Improved Nonlinearity Modeling beyond Standard Perturbation Theory

Abstract: We present a novel $n$EPT ($n$th-order Eulerian Perturbation Theory) scheme to model the nonlinear density field by the summation up to $n$th-order density fields in perturbation theory. The obtained analytical power spectrum shows excellent agreement with the results from all 20 Dark-Quest suites of $N$-body simulations spreading over a broad range of cosmologies. The agreement is much better than the conventional two-loop Standard Perturbation Theory and would reach out to $k_{\rm max}\simeq 0.4~h/{\rm Mpc}$ at $z=3$ for the best-fitting Planck cosmology, without any free parameters. The method can accelerate the forward modeling of the non-linear cosmological density field, an indispensable probe of cosmic mysteries such as inflation, dark energy, and dark matter.