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Nonlinear Power Spectrum Emulator

An emulator built from accurate N-body simulations to predict the nonlinear matter power spectrum with 1% accuracy up to k~1.h/Mpc, for cosmologies in the range of interest.

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Nonlinear Power Spectrum Emulator

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  1. Nonlinear Power Spectrum Emulator Christian Wagner in collaboration with Katrin Heitmann, Salman Habib, David Higdon, Brian Williams, Earl Lawrence (Los Alamos), and Martin White (Berkeley)

  2. (Tegmark & Zaldarriaga 2002)

  3. Motivation • Power spectrum is a key statistic in cosmology derived from the density field • Cosmology dependent, including Dark Energy and Theory of Gravity • Measured by various probes: Galaxy clustering (BAO), Lyman Alpha Forest, Cosmological Weak lensing, … • Precise theoretical predictions needed to derive unbiased cosmological parameter estimates from observational data • Huterer & Takada 2005: 1% accuracy needed for near-term WL experiments • Currently used fitting-formulas accurate to 5-10% (e.g. HaloFit by Smith et al. 2003) • Precision N-body simulations very expensive • MCMC needs to evaluate about 10,000 – 100,000 trial cosmologies => More than 30 years on current supercomputers

  4. Idea • Build an emulator from a “small” number of very accurate N-body simulations 1) Demonstrate 1% accuracy for a single cosmology (arxiv:0812.1052) 2) Develop framework of the emulator: simulation design, interpolation scheme, … (arxiv:0902:0429) 3) Build emulator from simulation suite and make it publicly available (almost done) • Problems: • At smaller scales (k>1 h/Mpc) baryonic physics becomes important (White 2004, Zhang & Knox 2004, Jing et al. 2006, Rudd et al. 2008) • High-dimensional parameter space => Choice of cosmological parameters and priors • Aim: Prediction of the nonlinear matter power spectrum out to k ~ 1 h/Mpc with 1% accuracy between z=0 and z=1 for flat wCDM cosmologies

  5. Convergence tests to assure 1% accuracy • Code comparison • Box size • Starting redshift • ICs (ZA or 2LPT) • Mass resolution • Time stepping • Force resolution • ~1 Gpc/h box with 10243 particles zstart~200 with ZA

  6. Cosmic Calibration Framework • Flat wCDM cosmologies: w, wm, wb, ns, and s8 • Priors from CMB and other probes • Hubble constant determined by CMB constraint: lA=pdlss/rs=302.4 (WMAP5) • Sampling the parameter space • Grid: e.g. 35=243 (not small), only 3 values per dimension • Random sampling produces clusters and voids in the parameter space • Orthogonal Array – Latin Hypercube sampling: space filling and good sampling in projected dimensions • Interpolation scheme: PC decomposition, Gaussian Process modeling

  7. 37 cosmological models

  8. Performance of the interpolation scheme HaloFit used as a proxy for the simulations

  9. Coyote Universe • 37 cosmological models • 16 low + 4 medium + 1 high-resolution simulation per model + perturbation theory for the largest scales • 11 outputs between z=4 and z=0 • ~ 800 simulations • ~ 60 Terabyte data • ~ 2 million CPU-hours • ~ six months on the Coyote cluster

  10. Holdout Test for 6 Models

  11. Out-of-Sample Test (LCDM)

  12. Conclusion & Outlook • Nonlinear matter power spectrum prediction accurate to 1% out to k~1 h/Mpc • Small number (~40) of cosmological models sufficient to cover the range of interest (5 parameters) • Use Coyote Emulator instead of HaloFit • LRG mock catalogs for BOSS • Emulator for the mass function instead of fitting formula? • Extend the parameter space to non-constant w? • Go beyond k = 1 h/Mpc?

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