High-precision predictions for the acoustic scale in the nonlinear regime

Hee Jong Seo, Jonathan Eckel, Daniel J. Eisenstein, Kushal Mehta, Marc Metchnik, Nikhil Padmanabhan, Phillip Pinto, Ryuichi Takahashi, Martin White, Xiaoying Xu

Research output: Contribution to journalArticlepeer-review

106 Scopus citations


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 1.5s 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 χ2 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 5000 h-3 Gpc3 of cosmological Particle-Mesh simulations from Takahashi et al. At an expected sample variance level of 1%, the agreement between the Fisher matrix estimates based on Seo and Eisenstein and the N-body results is better than 10%.

Original languageEnglish (US)
Pages (from-to)1650-1667
Number of pages18
JournalAstrophysical Journal
Issue number2
StatePublished - Sep 10 2010


  • Distance scale
  • Large-scale structure of universe
  • Methods: numerical

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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