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Probing the cosmic expansion with redshift distribution: prospects and theoretical challenges

Probing the cosmic expansion with redshift distribution: prospects and theoretical challenges. Yipeng Jing ( 景益鹏） Shanghai Jiaotong University Department of Physics and Astronomy. The “ Hubble diagram ” of Type Ia supernovae tells us that matter is not enough…. log( Distance d L ). a(t).

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Probing the cosmic expansion with redshift distribution: prospects and theoretical challenges

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  1. Probing the cosmic expansion with redshift distribution: prospects and theoretical challenges Yipeng Jing (景益鹏） Shanghai Jiaotong University Department of Physics and Astronomy

  2. The “Hubble diagram” of Type Ia supernovae tells us that matter is not enough… log(DistancedL) a(t) Perlmutter et al. 1999, Riess et al. 1998 Redshift of spectral lines Luigi Guzzo

  3. 为什么宇宙在加速膨胀？为什么存在暗能量？

  4. Cosmic Concordance • Large-Scale Structure/Clusters • Ωm =0.25-0.3 • Cosmic Microwave Background • Flat geometry (ΩTOT=1) • Ωm ~0.25 Ω> 0 • Supernovae • Accelerating expansion • Ω~ 1 (p=wρc2 , e.g. with w=-1 Vacuum energy) • Altogether (any two of them) • Ωm ~0.25 Ω~0.75

  5. Dark energy (ΩΛ) Matter (Ωm) Today Size=2 Size=1/2 Size=4 Size=1/4 Fine-tuning and Cosmic Coincidence If w=-1 and the cosmological constant corresponds to some sort of “quantum zero-point”, then its value today is a factor ~10120 too small, plus it is suspiciously fine-tuned: anthropic argument? redshift time z=3 z=1 Thus could we have w = w(z) ?--> e.g. quintessence, a cosmic scalar field slowly rolling to the minimum of its potential (e.g. Wetterich 1988), inducing an evolving -1 < w(z) < -1/3. Or more complex interactions between DM and DE (e.g. Amendola 2000; Liddle et al. 2008; He et al.) ?

  6. But we need to look at both sides of the story… Modify gravity theory [e.g. R f(R) ] Add dark energy “…the Force be with you”

  7. So, the equation of state is not the end of the story… Cosmic acceleration can also be explained by modifying the theory of gravity [as e.g. in f(R) theories, Capozziello et al. 2005, or in multi-dimensional “braneworld” models, Dvali et al. (DGP) 2000].  How to distinguish between these two options, observationally? Growth of linear density fluctuationsδ=δρ/ρ in the expanding Universe (in GR): which has a growing solution: from which we define agrowth rate • The growth equation (and thus the growth rate) depends not only on the expansion history H(t) (and thus on w) but also on the gravitation theory (e.g. Lue et al. 2004)

  8. 4个引力模型: GR，f(R)，DGP，TeVeS 张鹏杰等提出在宇宙学 尺度上检验广义相对论与其 他引力论的Eg方法

  9. Observational Probes • Supernovae M(z) • Baryon Acoustic Oscillations (BAO) • Abundance of rich clusters • Weak Lensing • Redshift distortion 3 of them can be accomplished with a redshift survey of galaxies

  10. 1亿个星系的照像图像；100万个星系的光谱－－Sloan Digital Sky Survey

  11. Distribution of galaxies （r<17.7) and luminous red galaxies in redshift space with Sloan Digital Sky Survey (Blanton and SDSS) Not real space!

  12. Growth of Large scales

  13. Cosmic expansion and peculiar velocity: observed redshift • Nearby Universe: zobs=z0 + vpeculirar/c • Distant Universe: zobs=(1+z0)(1+ vpeculirar/c) • Note: vpeculirar is the peculiar velocity along the line of sight; z0: gives a true real space distribution if the cosmology is known; • But vpeculirar is generally existing and difficult to be separated from z0, thus the distribution from zobsis distorted—redshift distortion

  14. Redshift distortion: bad or good • Peculiar velocity: induced by cosmic structures, therefore used to probe the growth of the structures; • Peculiar velocity: change structures along the line-of-sight only

  15. How much is the effect Linear regime---linear perturbation and distant observer • power spectrum is enhanced along the line-of sight • Ps(k)=P(k) (1+f μ2)2 [Kaiser 1987] f is the linear growth rate; μ is the cosine of the angle • Non-linear regime– virialized halo • e-(kσ/H)**2/2; σ is the velocity dispersion along z; can be elongated by 5-10 times (Finger of God effect)

  16. f = bLβ Compression parameter β(Kaiser 1987) Line of sight to observer Redshift-space galaxy-galaxy correlation function ξ(rp,π) Pair separation perpendicular to line-of-sight rp(h-1 Mpc) Full distortions, including small-scale “spindle” due to clusters of galaxies, Ωm=0.25, ΩΛ=0.75 No redshift distortions s π Pair separation along line-of-sight π (h-1 Mpc) rp Linear distortions only, flattening proportional to growth rate: depends on amount and kind of dark matter and dark energy

  17. 宇宙微波背景的温度分布 Baryon Acoustic Oscillations (BAO)

  18. WMAP 卫星观测5年所获得的微波背景温度分布的角功率谱； J. Dunkley et al. Astroph/08030586

  19. 宇宙复合时期辐射－重子流体的振荡（Baryon Acoustic Oscillations， BAO），也会留在暗物质的分布。由于星系在大尺度上的分布相对暗物质是线性偏袒（linearly biased），所以星系的空间分布也存在BAO，且其尺度不随时间（红移）演化，即是理想的标准尺子

  20. 两点相关函数 斯隆巡天亮红星系（Luminous Red Galaxies， LRG)的两点相关函数 D. J. Eisenstein et al., Astrophys. J. 619, 178 (2005).

  21. redshift distortion: cosmological and peculiar velocity Peculiar dynamic Cosmological geometric

  22. Possible Geometries of the Universe

  23. Observational Probes—with A redshift survey • Supernovae M(z) • Baryon Acoustic Oscillations (BAO) • Abundance of rich clusters • Weak Lensing • Redshift distortion

  24. We also consider the dependence on the information used: the full galaxy power spectrum P(k), P(k) marginalized over its shape, or just the Baryon Acoustic Oscillations (BAO). We find that the inclusion of growth rate information (extracted using redshift space distortion and galaxy clustering amplitude measurements) leads to a factor of 3 improvement in the FoM, assuming general relativity is not modified. This inclusion partially compensates for the loss of information when only the BAO are used to give geometrical constraints, rather than using the full P(k) as a standard ruler. We

  25. Observational Probes—with A redshift survey • Supernovae M(z) • Baryonic Acoustic Oscillations (BAO) • Abundance of rich clusters • Weak Lensing • Redshift distortion

  26. Measure the redshift cross correlation function for groups with a given central stellar mass (Li et al. 2012

  27. Constraint on cosmology σ8=0.84 ± 0.03 （03/2012）; well agrees with the 9-year data of WMAP （0.83 ± 0.02，12/2012）, also agree with the s-z of Planck (3/2013) Li,C, YPJ, etal.2012)

  28. Dark Energy Task Force • Established by AAAC and HEPAP as joint subcommittee to advise the 3 agencies: Report issued in September 2006 (astro-ph/0609591) • Defined stages of projects: • Stage I=completed • Stage II=on-going • Stage III=near-term, medium-cost, proposed: improve constraints by 3-5x • Stage IV=LSST, SKA, JDEM: improve constraints by 10x • Stage III experiments will also refine methods for Stage IV

  29. Observational status

  30. 1亿个星系的照像图像；100万个星系的光谱－－SDSS巡天1亿个星系的照像图像；100万个星系的光谱－－SDSS巡天

  31. SDSS survey III Current Status

  32. Before: Big Baryon Oscillation Spectroscopic Survey BigBOSSNow: Medium Scale – Dark Energy Spectroscopic Instrument MS-DESI (CD0 Approved by DOE)

  33. BigBOSS project • Construct BigBOSS instrument: • 3 deg diameter FOV prime focus corrector • 5000 fiber positioner • 10x3 spectrographs, 3400-10,600 Ang • Conduct BigBOSS Key Project • 495 nights at Mayall 4-m • 14,000 deg2 survey • 50,000,000 spectra • 20,000,000+ galaxy redshifts • 3,000,000+ QSOs David Schlegel, LBL, 1 Sep 2011

  34. China’s participation （from 2009.4） Positioner: the department of Precision Instruments, USTC Science: Shanghai Jiaotong University; Shanghai Astronomical Observatory;USTC/Astronomy; and other institutes can be included

  35. BigBOSS survey overview

  36. Wish List • Dark Energy and modified gravity: • BAO z=0 ➝ 3.5 • Redshift Space Distortions z=0 ➝ 3.5 • Particle Physics from Astronomy: Neutrino Masses • Inflation: Detect Non-Gaussianity All can be studied with a galaxy z-survey

  37. 1% precision BigBOSS science reach: BAO • Dark energy from Stage IV BAO • Geometric probe with 0.3-1% precision from z=0.5 -> 3 BigBOSS BAO precision Precision in measurement of size scale

  38. 上海交通大学、上海天文台和中国科大是成员单位上海交通大学、上海天文台和中国科大是成员单位

  39. Theoretical Challenges • Even with a huge sample of galaxy redshifts, there are challenges to model the power spectrums (two-point CFs) and extract the physical parameters (cosmological parameters, growth rate) etc • The challenge comes from the “precision” requirement

  40. The growth factor (scale-dependent bias included) Okumura, Jing 2011, ApJ

  41. Main causes Okumura, YPJ 2011; Zhang, P etal 2012 • Non-Linear Mapping: from real space to redshift space because of the non-linear coupling between position and velocity • Nonlinear evolution: of density and velocity fields • Non-linear and non-local galaxy-matter relation (Stochasticity)

  42. Quantifying • Correlation • 2) Nonlinearity • 3) Stochasticity Okumura,YPJ,2011

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