Probing the cosmic expansion with redshift distribution: prospects and theoretical challengesYipeng Jing (Shanghai Jiaotong UniversityDepartment of Physics and Astronomy

Perlmutter et al. 1999, Riess et al. 1998The Hubble diagram of Type Ia supernovae tells us that matter is not enoughlog(Distance dL)Redshift of spectral lines Luigi Guzzo

Cosmic ConcordanceLarge-Scale Structure/Clusters m =0.25-0.3 Cosmic Microwave Background Flat geometry (TOT=1) m ~0.25 > 0 SupernovaeAccelerating expansion ~ 1 (p=wc2 , e.g. with w=-1 Vacuum energy)Altogether (any two of them) m ~0.25 ~0.75

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?timeFine-tuning and Cosmic CoincidenceThus 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.) ?redshiftz=3z=1

But we need to look at both sides of the storyAdd dark energyModify gravity theory [e.g. R f(R) ]the Force be with you

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]. 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)

How to distinguish between these two options, observationally?Growth of linear density fluctuations =/ in the expanding Universe (in GR):

4: GRf(R)DGPTeVeSEg

Observational ProbesSupernovae M(z)Baryon Acoustic Oscillations (BAO)Abundance of rich clustersWeak LensingRedshift distortion3 of them can be accomplished with a redshift survey of galaxies

1100Sloan Digital Sky Survey

Distribution of galaxies r

Growth of Large scales

Nearby Universe: zobs=z0 + vpeculirar/cDistant 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 distortedredshift distortion

Cosmic expansion and peculiar velocity: observed redshift

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

How much is the effectLinear regime---linear perturbation and distant observerpower spectrum is enhanced along the line-of sightPs(k)=P(k) (1+f 2)2 [Kaiser 1987] f is the linear growth rate; is the cosine of the angleNon-linear regime virialized haloe-(k/H)**2/2; is the velocity dispersion along z; can be elongated by 5-10 times (Finger of God effect)

Pair separation perpendicular to line-of-sight rp (h-1 Mpc)Pair separation along line-of-sight (h-1 Mpc)Linear distortions only, flattening proportional to growth rate: depends on amount and kind of dark matter and dark energyFull distortions, including small-scale spindle due to clusters of galaxies,m=0.25, =0.75No redshift distortionsRedshift-space galaxy-galaxy correlation function (rp,)rps

Baryon Acoustic Oscillations (BAO)

WMAP 5

J. Dunkley et al.Astroph/08030586

Baryon Acoustic Oscillations BAOlinearly biasedBAO

Luminous Red Galaxies LRG)D. J. Eisenstein et al., Astrophys. J. 619, 178 (2005).

redshift distortion: cosmological and peculiar velocityCosmologicalgeometric Peculiardynamic

Possible Geometries of the Universe

Observational Probeswith A redshift surveySupernovae M(z)Baryon Acoustic Oscillations (BAO) Abundance of rich clustersWeak LensingRedshift distortion

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

Observational Probeswith A redshift surveySupernovae M(z)Baryonic Acoustic Oscillations (BAO) Abundance of rich clustersWeak LensingRedshift distortion

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

Constraint on cosmology8=0.84 0.03 03/2012; well agrees with the 9-year data of WMAP 0.83 0.0212/2012, also agree with the s-z of Planck (3/2013)Li,C, YPJ, etal.2012)

Dark Energy Task ForceEstablished 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=completedStage II=on-going Stage III=near-term, medium-cost, proposed: improve constraints by 3-5xStage IV=LSST, SKA, JDEM: improve constraints by 10xStage III experiments will also refine methods for Stage IV

Observational status

1100SDSS

SDSS survey III

Current Status

Before: Big Baryon Oscillation Spectroscopic Survey BigBOSS

Now: Medium Scale Dark Energy Spectroscopic Instrument MS-DESI (CD0 Approved by DOE)

David Schlegel, LBL, 1 Sep 2011Construct BigBOSS instrument:3 deg diameter FOV prime focus corrector5000 fiber positioner10x3 spectrographs, 3400-10,600 Ang

Conduct BigBOSS Key Project495 nights at Mayall 4-m14,000 deg2 survey50,000,000 spectra 20,000,000+ galaxy redshifts 3,000,000+ QSOsBigBOSS project

Chinas participation from 2009.4Positioner: the department of Precision Instruments, USTCScience: Shanghai Jiaotong University; Shanghai Astronomical Observatory;USTC/Astronomy; and other institutes can be included

BigBOSS survey overview

Wish ListDark Energy and modified gravity: BAO z=0 3.5Redshift Space Distortions z=0 3.5Particle Physics from Astronomy: Neutrino MassesInflation: Detect Non-GaussianityAll can be studied with a galaxy z-survey

BigBOSS science reach: BAODark energy from Stage IV BAOGeometric probe with 0.3-1% precision from z=0.5 -> 3BigBOSS BAO precisionPrecision in measurement of size scale

Theoretical ChallengesEven 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) etcThe challenge comes from the precision requirement

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

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

Okumura,YPJ,2011QuantifyingCorrelation

2) Nonlinearity

3) Stochasticity

Many more references thereinOkumura, Seljak, McDonald & Desjacques (2012) JCAP 02, 010Okumura, Seljak & Desjacques (2012) JCAP 11, 014Vlah, Seljak, McDonald, Okumura & Baldauf (2012) JCAP 11, 009Vlah, Seljak, Okumura & Desjacques (2013) submitted to JCAP

One solution Decompose the velocity field into v(x) = v(x) +vS(x) + vB(x) (E-B modes; E modes correlated or non-correlated with density; Zhang, P. et al. 2012) Zheng, Y. et al. 2013

RemarksCosmic expansion is accelerating redshift survey explores the geometry and the structure growth Large redshift surveys, such as MS-DESI and Euclid, are coming around 2020Precision modeling of the redshift distortion at the required levels is still challenging theorists

Thanks!

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