Pengjie ZhangShanghai 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.

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Velocity BiasChallenge/opportunity to peculiar velocity cosmology

张鹏杰 ZHANG, Pengjie

ZPJ, Zheng & Jing, 2014, arXiv: 1405.7125

Zheng, ZPJ & Jing, 2014a, arXiv: 1409.6809

Zheng, ZPJ & Jing, 2014b, arXiv: 1410.1256

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Sampling artifact

Velocity bias

Hard works are done by Zheng Yi, my student just graduated.

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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

peculiarvelocity

v=Hr v=Hr

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Peculiar velocity: unique probe of cosmologyAt 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

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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. 1404.3799)– Statistical errors blow up with redshift. Only applicable at z<0.1– Systematic errors (e.g. 6dF, Magoulas et al. 1206.0385).

• 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. 2011 )– Relativistic effect in galaxy size/flux/magnification bias: only applicable

at low z (e.g. Bonvin, 2008. But see ZPJ & Chen 2008)– Redshift space distortion: very promising….

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Measure peculiar velocity at cosmological distanceheuristic approach

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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

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• 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. 2002 on 2dF; Tegmark et al. 2004, on SDSS; etc. )

After layers of approximations,

Often further compressed into a single number

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Chuang et al. 1312.4889

• 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

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Velocity bias: potential systematic error

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• A first order systematic error in cosmology– Have to understand the velocity bias to 1% level

accuracy at k~0.1h/Mpc.

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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?

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Severe sampling artifactcan be misinterpreted as a “velocity bias”

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• Naive comparison between the raw measurements of halo velocity and DM velocity gives a apparent bv<1

• Illusion caused by the sampling artifact

• Unphysical numerical effect. But can be misinterpreted as a “velocity bias”

Zheng, ZPJ, Jing, 2014b

DM

Halo

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Yipeng’s P3M simulation: 1200 Mpc/h, 10243 particles

Detection of the sampling artifact in DM velocity field

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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

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• 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

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?

Understanding the sampling artifact

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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, 2014aZPJ, Zheng & Jing, 2014

Theory and simulation of the sampling artifact

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Theory prediction:ZPJ, Zheng & Jing, 2014

Simulation verificationZheng, ZPJ & Jing, 2014a

The measured velocity power spectrumThe real velocity power spectrum

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Sampling artifact: theory vs. simulation

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Raw measurement

Step two correction

Step oneCorrection

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1. Velocity bias vanishes at k<0.1 h/Mpc. Consolidates peculiar velocity cosmology2. Velocity bias at k>0.1h/Mpc? Poses a challenge

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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)

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