Accuracy of Cosmological N -body Simulations

1. Raw results DARK ENERGY Ludwig-Maximilians-University, Munich Takahiro Nishimichi (the Univ. of Tokyo) Accuracy of Cosmological N-body Simulations 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? 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