1. Christian Wagner - September 24 2009 - Potsdam 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. Christian Wagner - September 24 2009 - Potsdam (Tegmark & Zaldarriaga 2002)

3. Christian Wagner - September 24 2009 - Potsdam Motivation Power spectrum is a key statistic in cosmology Power spectrum is a key statistic in cosmology derived from the density field Cosmology dependent, including Dark Energy and Theory of Gravity Cosmology dependent, including Dark Energy and Theory of Gravity Measured by various probes: Galaxy clustering (BAO), Lyman Alpha Forest, Cosmological Weak lensing, … 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 Precise theoretical predictions needed to derive unbiased cosmological parameter estimates from observational data Huterer & Takada 2005: 1% accuracy needed for near-term WL experiments 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) Currently used fitting-formulas accurate to 5-10% (e.g. HaloFit by Smith et al. 2003) Precision N-body simulations very expensive Precision N-body simulations very expensive MCMC needs to evaluate about 10,000 – 100,000 trial cosmologies MCMC needs to evaluate about 10,000 – 100,000 trial cosmologies => More than 30 years on current supercomputers

4. Christian Wagner - September 24 2009 - Potsdam Idea Build an emulator from a “small” number of very accurate N-body simulations 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: 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) 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 High-dimensional parameter space => Choice of cosmological parameters and priors => Choice of cosmological parameters and priors Aim: Prediction of the nonlinear matter power spectrum 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. Christian Wagner - September 24 2009 - Potsdam Convergence tests to assure 1% accuracy Code comparison Code comparison Box size Box size Starting redshift Starting redshift ICs (ZA or 2LPT) ICs (ZA or 2LPT) Mass resolution Mass resolution Time stepping Time stepping Force resolution Force resolution  ~1 Gpc/h box with 1024 3 particles z start ~200 with ZA

6. Christian Wagner - September 24 2009 - Potsdam Cosmic Calibration Framework Flat wCDM cosmologies: w,  m,  b, n s, and  8 Flat wCDM cosmologies: w,  m,  b, n s, and  8 Priors from CMB and other probes Priors from CMB and other probes Hubble constant determined by CMB constraint: l A =  d lss /r s =302.4 (WMAP5) Hubble constant determined by CMB constraint: l A =  d lss /r s =302.4 (WMAP5) Sampling the parameter space Sampling the parameter space Grid: e.g. 3 5 =243 (not small), only 3 values per dimension Grid: e.g. 3 5 =243 (not small), only 3 values per dimension Random sampling produces clusters and voids in the parameter space Random sampling produces clusters and voids in the parameter space Orthogonal Array – Latin Hypercube sampling: Orthogonal Array – Latin Hypercube sampling: space filling and good sampling in projected dimensions Interpolation scheme: PC decomposition, Gaussian Process modeling Interpolation scheme: PC decomposition, Gaussian Process modeling

7. Christian Wagner - September 24 2009 - Potsdam 37 cosmological models

8. Christian Wagner - September 24 2009 - Potsdam Performance of the interpolation scheme HaloFit used as a proxy for the simulations

9. Christian Wagner - September 24 2009 - Potsdam Coyote Universe 37 cosmological models 37 cosmological models 16 low + 4 medium + 1 high-resolution simulation per model + perturbation theory for the largest scales 16 low + 4 medium + 1 high-resolution simulation per model + perturbation theory for the largest scales 11 outputs between z=4 and z=0 11 outputs between z=4 and z=0  ~ 800 simulations  ~ 60 Terabyte data  ~ 2 million CPU-hours  ~ six months on the Coyote cluster

10. Christian Wagner - September 24 2009 - Potsdam Holdout Test for 6 Models

11. Christian Wagner - September 24 2009 - Potsdam Out-of-Sample Test (  CDM)

12. Christian Wagner - September 24 2009 - Potsdam Conclusion & Outlook Nonlinear matter power spectrum prediction accurate to 1% out to k~1 h/Mpc 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) Small number (~40) of cosmological models sufficient to cover the range of interest (5 parameters) Use Coyote Emulator instead of HaloFit Use Coyote Emulator instead of HaloFit LRG mock catalogs for BOSS LRG mock catalogs for BOSS Emulator for the mass function instead of fitting formula? Emulator for the mass function instead of fitting formula? Extend the parameter space to non-constant w? Extend the parameter space to non-constant w? Go beyond k = 1 h/Mpc? Go beyond k = 1 h/Mpc?