HIGH-PRECISION PREDICTIONS FOR THE ACOUSTIC SCALE IN THE NONLINEAR REGIME

Abstract

We measure shifts of the acoustic scale due to nonlinear growth and redshift\ndistortions to a high precision using a very large volume of\nhigh-force-resolution simulations. We compare results from various sets of\nsimulations that differ in their force, volume, and mass resolution. We find a\nconsistency within 1.5-sigma for shift values from different simulations and\nderive shift alpha(z) -1 = (0.300\\pm 0.015)% [D(z)/D(0)]^{2} using our fiducial\nset. We find a strong correlation with a non-unity slope between shifts in real\nspace and in redshift space and a weak correlation between the initial redshift\nand low redshift. Density-field reconstruction not only removes the mean shifts\nand reduces errors on the mean, but also tightens the correlations: after\nreconstruction, we recover a slope of near unity for the correlation between\nthe real and redshift space and restore a strong correlation between the low\nand the initial redshifts. We derive propagators and mode-coupling terms from\nour N-body simulations and compared with Zeldovich approximation and the shifts\nmeasured from the chi^2 fitting, respectively. We interpret the propagator and\nthe mode-coupling term of a nonlinear density field in the context of an\naverage and a dispersion of its complex Fourier coefficients relative to those\nof the linear density field; from these two terms, we derive a signal-to-noise\nratio of the acoustic peak measurement. We attempt to improve our\nreconstruction method by implementing 2LPT and iterative operations: we obtain\nlittle improvement. The Fisher matrix estimates of uncertainty in the acoustic\nscale is tested using 5000 (Gpc/h)^3 of cosmological PM simulations from\nTakahashi et al. (2009). (abridged)\n