Pengjie Zhang Shanghai Jiao Tong University The large scale structure and its cosmological applications The Sunyaev Zel’dovich effect (2001-present) – Missing baryons, dark flow, vacuum decay, bubble collision – The thermal and kinetic SZ tomography Weak gravitational lensing (2003-present) – Systematics in theory (Born deviation, lens-lens, source-lens (see Yu Yu’s talk on Oct. 11), baryons, etc.) – Systematics in observation and self-calibration (2010) Self-calibrating photo-z and intrinsic alignment – Mapping dark matter with cosmic magnification (2005-present) Not background-foreground cross correlation works in the literature Redshift space distortion (2007-present) – Theoretical modeling and velocity reconstruction – Velocity statistics (see my talk on Oct. 9) Cosmological tests of fundamental cosmology – GR, the Copernican Principle, origin mechanism, etc. 1 THCA,

Velocity Bias Challenge/opportunity to peculiar velocity cosmology 张鹏杰 ZHANG, Pengjie ZPJ, Zheng & Jing, 2014, arXiv: Zheng, ZPJ & Jing, 2014a, arXiv: Zheng, ZPJ & Jing, 2014b, arXiv: THCA, Sampling artifact Velocity bias Hard works are done by Zheng Yi, my student just graduated.

3 Peculiar velocity: a window to the dark universe Matter distribution in our universe is inhomogeneous Gravitational attraction arising from inhomogeneity perturbs galaxies and causes deviation from the Hubble flow v r v r peculiar velocity v=Hr THCA,

4 Peculiar velocity: unique probe of cosmology At scales larger than galaxy clusters, directly probes gravity ( t-t component: In linear regime, honest tracer of matter distribution Necessary for the complete phase-space description of the universe THCA,

Challenges However, accurate velocity measurement? In particular at cosmological distance, e.g. z~1? Conventional method: subtract the Hubble flow with distance indicators (FP, TF). – E.g. SFI++, 6dF (e.g. Johnson et al ) – Statistical errors blow up with redshift. Only applicable at z<0.1 – Systematic errors (e.g. 6dF, Magoulas et al ). New methods – Kinetic Sunyaev Zel’dovich effect: bias from baryon mass – SNe Ia: statistical errors blow up with z; contamination from lensing – Relativistic effects in galaxy number density: only detectable at horizon scales (e.g. Yoo et al ) – Relativistic effect in galaxy size/flux/magnification bias: only applicable at low z (e.g. Bonvin, But see ZPJ & Chen 2008) – Redshift space distortion: very promising…. 5

Measure peculiar velocity at cosmological distance heuristic approach 6 Directly measurableAlso directly measurable! Peculiar velocity can be reconstructed ! Not only the average statistics, but also the 3D field Real space power spectrum Redshift space power spectrum

7 Through the anisotropy in the redshift space power spectrum, one can reconstruct the velocity power spectrum Has been applied to real data (Tegmark et al on 2dF; Tegmark et al. 2004, on SDSS; etc. ) After layers of approximations,

Often further compressed into a single number 8 Chuang et al Will be improved significantly by eBOSS To 1% by stage IV surveys such as DESI, Euclid and SKA

Velocity bias or not? A fundamental problem in peculiar velocity cosmology THCA,

Velocity bias: potential systematic error 10 A first order systematic error in cosmology – Have to understand the velocity bias to 1% level accuracy at k~0.1h/Mpc. THCA,

11 Peculiar velocity cosmology by default assumes no velocity bias at large scale: Environmental effect: halos/galaxies locate at special regions around density peaks. Proto-halos/linearly evolved density peaks (BBKS 1986; Desjacques & Sheth 2010) have velocity bias What would be the velocity bias of halos in simulations? THCA,

Severe sampling artifact can be misinterpreted as a “velocity bias” 12 Naive comparison between the raw measurements of halo velocity and DM velocity gives a apparent b v <1 Illusion caused by the sampling artifact Unphysical numerical effect. But can be misinterpreted as a “velocity bias” Zheng, ZPJ, Jing, 2014b DM Halo THCA, Yipeng’s P 3 M simulation: 1200 Mpc/h, particles

Detection of the sampling artifact in DM velocity field THCA, DM control samples: Randomly select a fraction of DM simulations particles. By construction, the control samples and the FULL sample should have identical velocity. Therefore any difference is the result of sampling artifact. Zheng, ZPJ, Jing, 2014a

The sampling artifact 14 Where there is no particle, the velocity is usually non-zero. It can be large. The sampling on the volume weighted velocity field is biased/imperfect The sampling artifact: inevitable for inhomogeneously distributed objects. Severe for sparse populations. Persists for NP, Voronoi and Delaunay tessellation. The sampling and the signal are neither completely uncorrelated nor completely correlated. Hard to correct straightforwardly Can be fully described in the language of the D field (ZPJ, Zheng & Jing, 2014), similar to CMB lensing THCA, ?

Understanding the sampling artifact THCA, Including the correlation in D.Not exact. Neglect correlation in D Neglect v-D correlation. Our model works. But improvements are needed Take correlation in D fully into account Take v-D correlation into account Zheng, ZPJ & Jing, 2014a ZPJ, Zheng & Jing, 2014

Theory and simulation of the sampling artifact 16 Theory prediction: ZPJ, Zheng & Jing, 2014 Simulation verification Zheng, ZPJ & Jing, 2014a The measured velocity power spectrum The real velocity power spectrum THCA,

17 Sampling artifact: theory vs. simulation

18 Raw measurement Step two correction Step one Correction THCA,

1. Velocity bias vanishes at k 0.1h/Mpc? Poses a challenge 19 THCA,

For discussions Needs theory explanation Needs more accurate quantification – Need improved understanding of the sampling artifact Needs to extend to galaxies (mock catalog) Perhaps needs new velocity assignment (e.g. Jun Zhang’s idea) Cosmological applications – Could be smoking guns of MG – Promising tests of the equivalence principle (ongoing work with Zheng Yi, Yipeng, Baojiu Li & De-Chang Dai) THCA,