Accuracy of Cosmological N-body Simulations DARK ENERGY Ludwig-Maximilians-University, Munich Accuracy of Cosmological N-body Simulations Takahiro Nishimichi (the Univ. of Tokyo) Introduction BAOs (Baryon Acoustic Oscillations) A promising tool to access dark energy. Demand for more accurate theoretical modeling Nonlinearity of gravitational structure formation Redshift-space distortion Galaxy biasing Methods Perturbation theory Newly developed renormalized perturbation theory N-body simulations 1% error on BAO scale -> 3~5% Error on DE e.o.s. Is the currently achieved accuracy enough? Raw results Our simulations After correction 2LPT Gadget2 SPT: standard perturbation theory RPT: renormalized perturbation theory (Crocce+Scoccimarro06a,b,08) CLA: closure approximation (Taruya+Hiramatsu08) LIN: linear theory Convergence test is difficult from this figure because of large errorbars due to small total volume of N-body simulations (4h-3Gpc3). Errorbars largely reduced to sub-percent level! The three nonlinear models and N-body simulations agree at largest scales (k<0.05hMpc-1). RPT, CLA and N-body simulations agree within errorbars in almost the same range for a given redshift. RPT and CLA have better convergence properties than SPT in the plotted ranges. Correction for finiteness of volume Errorbars: Convergence regime Recovery of BAOs 2pt correlation (preliminary) C is a constant to be determined. Preliminary M08: Matsubara08 SK07: Sefusatti+Komatsu07 JK06: Jeong+Komatsu06 We construct smooth reference spectra using B-spline fit. (e.g., Percival+07, Nishimichi+07) The convergence regimes for the extracted BAO phases are wider than those for the amplitudes of P(k) (vertical arrows). The scale shift parameter α can be constrained tightly using the modes within our convergence regimes alone. The number of N-body realizations increased to 30. A good convergence in real space? Monopole and quadrupole moments are reasonably converged in redshift space? We determined the 1% and 3% convergence regimes where theoretical predictions and N-body simulations agree within 1% and 3%. Our formula explains the results (symbols) very well. Apendix: convergence test of our simulations Initial condition SPT w/o cutoff scale N-body code Fake agreement of SPT for small boxsize boxsize 2LPT vs. ZA RPT w/ cutoff scale