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 distortions to a high precision using a very large volume of high-force-resolution simulations. We compare results from various sets of simulations that differ in their force, volume, and mass resolution. We find a consistency within 1.5 − σ for shift values from different simulations and derive shift α(z) − 1 = (0.300 ± 0.015)%[D(z)/D(0)] 2 using our fiducial set. We find a strong correlation with a non-unity slope between shifts in real space and in redshift space and a weak correlation between the initial redshift and low redshift. Density-field reconstruction not only removes the mean shifts and reduces errors on the mean, but also tightens the correlations. After reconstruction, we recover a slope of near unity for the correlation between the real and redshift space and restore a strong correlation between the initial and the low redshifts. We derive propagators and mode-coupling terms from our N-body simulations and compare with the Zel'dovich approximation and the shifts measured from the χ 2 fitting, respectively. We interpret the propagator and the mode-coupling term of a nonlinear density field in the context of an average and a dispersion of its complex Fourier coefficients relative to those of the linear density field; from these two terms, we derive a signal-to-noise ratio of the acoustic peak measurement. We attempt to improve our reconstruction method by implementing 2LPT and iterative operations, but we obtain little improvement. The Fisher matrix estimates of uncertainty in the acoustic scale is tested using 5000h −3 Gpc 3 of cosmological PM simulations from Takahashi et al. (2009a). At an expected sample variance level of 1%, the agreement between the Fisher matrix estimates based on and the N-body results is better than 10 %. Subject headings: distance scale-large-scale structure of universe -methods: numerical

Observational probes of cosmic acceleration

“…This gives considerable freedom to fit away broadband nuisance terms while not impacting the acoustic peak. Seo et al (2010b) show stable results for α for various choices, e.g., polynomials of different order. Similarly, α is robust to changes in the choice of Σ NL , so one is not sensitive to how one estimates that parameter in simulations or mock catalogs.…”

“…N-body simulations reveal a similar story. Seo et al (2010b) measure the shift in the acoustic scale in a large volume of simulations and detect a shift from α = 1 of 0.3% ± 0.015% at z = 0.0, with a scaling in redshift proportional to the square of the linear growth function as expected for a second order effect (left panel of figure 12). validate their analytic calculation with a similar set of simulations.…”

“…(Left) Shifts of the acoustic scale in the redshift-space matter power spectrum versus redshift from Seo et al (2010b). The open symbols show the acoustic scale shifts prior to reconstruction; the dashed lines show a scaling of the square of the linear growth function.…”

“…Figure 13, from Padmanabhan et al (2012), illustrates how reconstruction works in the idealized case of an initial perturbation that exactly mimics the "acoustic ring" pattern. Seo and Eisenstein (2007) and Seo et al (2010b) investigate the effects of reconstruction in more detail, showing that it noticeably improves the scatter and decreases the shift of the recovered acoustic scale from the matter density field of N-body simulations. The latest simulations demonstrate that the non-linear shift of the scale has been removed to 0.02% or better (see Figure 12, left).…”

“…This procedure has been carried out by several different authors. For example, Seo and Eisenstein (2007) and and Seo et al (2010b) fit the measured power spectrum to the form…”