Cosmology on small scales: Emulating galaxy clustering and galaxy-galaxy lensing into the deeply nonlinear regime Ben Wibking Department of Astronomy Ohio State University with Andres Salcedo, David Weinberg, Lehman Garrison, Douglas Ferrer, Jeremy Tinker, Daniel Eisenstein, Marc Metchnik, and Philip Pinto
Why do we care? Is there a discrepancy between high-redshift and low-redshift probes of cosmology? PLANCK measurements favor a (marginally) higher amplitude of matter fluctuations than WMAP Some weak lensing analyses (e.g., CFHTLens, KiDS) have favored a (significantly) lower amplitude of matter fluctuations If found, tension is ~2σ, depending on the analysis (S 8 / 8 0.5 m ) Figure: DES Collaboration
Galaxy-galaxy lensing Source plane Lensing plane 100 60 Image plane 40 80 0 20 40 x (h 1 60 Mpc) 80 100 60 1 0 Mpc) 20 y (h Image: Hubble Deep Field (for illustrative purposes only) y (h 1 Mpc) 80 40 20 lens galaxies 0 0 20 40 x (h 1 60 Mpc) 80
Small scale systematics? Figures: Leauthaud+ 2017
Halo occupation distribution (HOD) 10 2 centrals satellites fiducial model mean number of galaxies hn Mhi 10 0 2 3 4 5 6 halo mass M h (h 1 M ) e.g. Berlind & Weinberg (2002)
Halo occupation distribution (HOD) 10 2 n gal = 0.00027 n gal = 0.00033 n gal mean number of galaxies hn Mhi 10 0 2 3 4 5 6 halo mass M h (h 1 M )
Halo occupation distribution (HOD) 10 2 log M = 0.58 log M = 0.78 log M mean number of galaxies hn Mhi 10 0 2 3 4 5 6 halo mass M h (h 1 M )
Halo occupation distribution (HOD) 10 2 M 1 M min = 9.05 M 1 M min = 10.05 M 1 /M min mean number of galaxies hn Mhi 10 0 2 3 4 5 6 halo mass M h (h 1 M )
Halo occupation distribution (HOD) 10 2 = 1.0 = 1.30 mean number of galaxies hn Mhi 10 0 2 3 4 5 6 halo mass M h (h 1 M )
Halo occupation distribution (HOD) 10 2 q env = -0.1 (high density environment) q env = -0.1 (low density environment) Q env mean number of galaxies hn Mhi 10 0 2 3 4 5 6 halo mass M h (h 1 M ) Makes <N Mh> a function of ~8 Mpc/h-scale overdensity
Emulator methodology 1. Run 40 N-body simulations with different cosmological parameters chosen from within the Planck 2015 wcdm allowed space (currently only a subset involving σ 8, Ω M ) 2. Populate dark matter halos with galaxies according to a phenomenological model of galaxy counts as a function of halo mass and environmental density (extended HOD model) 3. Compute the galaxy auto-correlation function and galaxy-matter cross-correlation function 4. Interpolate ( emulate ) between models across the allowed parameter space 5. Compute projection integrals to obtain observables w p and γ t
Emulator methodology 1. Run 40 N-body simulations with different cosmological parameters chosen from within the Planck 2015 wcdm allowed space (currently only a subset involving σ 8, Ω M ) 2. Populate dark matter halos with galaxies according to a phenomenological model of galaxy counts as a function of halo mass and environmental density (extended HOD model) 3. Compute the galaxy auto-correlation function and galaxy-matter cross-correlation function 4. Interpolate ( emulate ) between models across the allowed parameter space 5. Compute projection integrals to obtain observables w p and γ t
Emulator methodology Interpolating between models this can be nontrivial: Introduced to cosmology by the CosmicEmu Gaussian process interpolation of the nonlinear power spectrum obtained from simulations (Heitmann+ 2009) We instead interpolate various scale-dependent quantities using a (1st- or 2nd-order) Taylor expansion (similar to methodology of Mandelbaum+ 2013): scale-dependent bias b g, (scale-dependent) correlation coefficient r gm, and (scale-dependent) ratio of the nonlinear-to-linear matter correlation function (we denote this b nl )
Galaxy-galaxy lensing and clustering signal on scales 0.5 < r p < 30 Mpc/h fiducial + 8 + m fiducial + 8 + m wp (Mpc h 1 ) 10 2 t 10 3 10 4 10 0 r p (h 1 Mpc) 10 0 r p (h 1 Mpc)
HOD (satellite Mhalo) Assembly bias 1.20 1.20 1.20 fiducial (M1 /Mmin = 9.55) M1 /Mmin = 9.05 1.15 fiducial (q = 0) q = 0.1 q = +0.1 1.15 M1 /Mmin = 10.05 1.00 0.95 t 1.10 1.05 ratio of t 1.05 0.90 1.00 0.95 0.90 0.85 100 0.80 101 1 100 1 M1 /Mmin = 9.05 1.15 M1 /Mmin = 10.05 1.00 0.95 fiducial (q = 0) q = 0.1 q = +0.1 1.05 1.00 0.95 0.95 0.85 0.85 rp (h 1 Mpc) fiducial ( 8 = 0.78 8 = 0.88 1.00 0.85 0.80 8 = 0.83) Mpc) 1.05 0.90 101 1 1.10 0.90 100 = 0.83) 101 1.15 0.90 0.80 8 1.20 ratio of wp 1.05 100 rp (h 1.10 ratio of wp 1.10 fiducial ( 8 = 0.78 8 = 0.88 Mpc) 1.20 1.15 0.95 0.80 101 rp (h fiducial (M1 /Mmin = 9.55) 1.00 0.85 Mpc) 1.20 1.05 0.90 0.85 rp (h ratio of wp 1.15 1.10 ratio of ratio of t 1.10 0.80 Cosmology 100 101 rp (h 1 Mpc) 0.80 100 101 rp (h 1 Mpc)
Covariance matrices and forecasting for LOWZ GGL with SDSS imaging 1.4 w p 1.0 1.4 t 1.0 1.2 1.0 0.8 1.2 1.0 0.8 log rp (h 1 Mpc) 0.8 0.6 0.4 0.2 0.0 0.6 0.4 0.2 log rp (h 1 Mpc) 0.8 0.6 0.4 0.2 0.0 0.6 0.4 0.2 0.2 0.0 0.5 1.0 log r p (h 1 Mpc) 0.0 0.2 0.0 0.5 1.0 log r p (h 1 Mpc) 0.0 (ngal = 3 x 10-4 h 3 Mpc -3, ~1 galaxy arcmin -2 )
Cosmological constraints forecasted: 1.8% uncertainty on σ 8 Ω m 0.58 Using only scales >2 Mpc/h (lensing) and >4 Mpc/h (clustering), the constraints degrade to 3.8% More precise constraints by a factor of >2, equivalent to >4x the survey area without small scales ln log M ln M 1 Mmin ln qenv ln m ln 8 0.1 0.0 0.1 0.2 0.0 0.2 0.15 0.00 0.15 0.03 0.00 0.03 0.6 0.3 0.0 0.3 0.6 0.08 0.00 0.08 0.05 0.00 0.05 =0.049 Substantial gains in information from small scales =0.094 =0.185 =0.109 =0.028 =0.298 =0.066 =0.042 0.05 0.00 0.05 0.1 0.0 0.1 0.2 0.0 0.2 0.15 0.00 0.15 0.03 0.00 0.03 0.6 0.3 0.0 0.3 0.6 0.08 0.00 0.08 0.05 0.00 0.05 ln n gal ln log M ln M 1 M min ln q env ln m ln 8
fiducial 10x source density excluding w p < 5 h 1 Mpc What is the cost of marginalizing over galaxy formation uncertainties? marginalized fractional uncertainty in 8 10 2 8 n gal log M q env M 1 M min cumulatively (from the left) marginalized parameters m
Conclusions Cosmology on small scales is promising, but will depend on control of astrophysical systematics We can verify that our recovery of cosmology is unbiased with mock cosmological analysis of hydrodynamic simulations, other models of galaxy formation that are completely different We can test and rule out models of the galaxy-halo occupation jointly with cosmological models The future: considering additional cosmological parameters using the full grid of simulations, fitting to CMASS + DES lensing measurements
Questions?