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2010 年十年领悟 [ 见解 ] 和十大突破. 《 科学 》. 精确宇宙学. 世纪之交 -----3 朵乌云: 3D 宇宙. [eprint arXiv:1010.1307]. 3D Universe.

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[eprint arXiv:1010.1307]

3D Universe



  • 1为什么!
  • 2是什么!
  • 3应该是什么!


  • H(z)
  • the observational Hubble parameter data (OHD)
  • 张同杰 马骢 [2010级硕士]
  • 北京师范大学天文系
  • Hubble Parameter Cosmology or H(z) Cosmology
lensing cosmology
Lensing cosmology

Lee Jounghun, Pen,Ue-Li. ApJ, 686: L1–L4, 2008

simulation weak lensing wavelet
Simulation, Weak lensing,Wavelet

Zhang, Tong-Jie; Yu, Hao-Ran; et al, ApJ, 728, 35

Yu, Hao-Ran; Zhang, Tong-Jie et al arXiv:1012.0444

luminosity distance vs hubble parameter
Luminosity distance VS Hubble parameter
  • 1. The integral smears out information about E o S
  • 2. The integral make the luminosity distance have only a weak

discriminating power with respect to different possible histories of E o S

  • 一. Observational methods for H(z)
  • 二. Power of Observational Hubble parameter data[OHD] -- H(z)
  • 三、Future of OHD
observational methods for h z
一. Observational methods for H(z)
  • 1. the differential age method: different age of the oldest galaxies in each redshift bin;
  • 2. the radial BAO size method: the baryon acoustic oscillation (BAO) along the

line-of-sight direction from the spectroscopic galaxy samples;

  • 3. the GW method: compact-binary object- observation.
1 the differential age method
1. the differential age method
  • 1. Measure the age difference, Dt, between two passively evolving galaxies that formed at the same time but are separated by a small redshift interval Dz;
  • 2. Infer the derivative dz/dt from the ratio Dz/Dt.
  • At high redshifts, z=1–2, H(z) would constrain the EoS of DE, while at low redshifts, z<0.2, it would determine the Hubble constant, H_0.
galaxies samples the fair samples of passively evolving galaxies
Galaxies samples:The fair samples of passively evolving galaxies
  • 1.Similar metallicities
  • 2. Low star formation rates (i.e., a red color)

So, the average age of their stars would far exceed the age difference between the two galaxy samples.

joan simon licia verde and raul jimenez upenn prd 71 123001 2005
Joan Simon,Licia Verde, and Raul Jimenez [upenn]. PRD 71, 123001 (2005)

9 data point = 8+1

  • 1 data---Sloan Digital Sky Survey(SDSS)[R. Jimenez et al, ApJ.593, 622 (2003)]
  • 8 data----GeminiDeep Survey (GDDS) survey [R. G. Abraham et al., Astron. J. 127, 2455(2004)] and archival data [T. Treuet al, MNRAS. 308, 1037 (1999)]
key advantage
Key advantage
  • Differential ages are less sensitive to systematics errors than absolute ages.
two new h z data sets
Two new H(z) data sets
  • Stern, D., Jimenez, al. 2010, JCAP 02(2010)008[astro-ph/0907.3149]
  • Two samples: 1. the SPICES sample. Most of the spectra were taken at the Keck telescope; 2. The VVDS [49] is the VIMOS-VLT survey carried out by the VLT/ESO telescope
  • 1+8+2=11
2 the radial bao size method
2. the radial BAO size method
  • the baryon acoustic oscillation (BAO) along the line-of-sight direction from the spectroscopic galaxy samples

Looking back in time; angles imply distance

standard ruler



Detection of BAO

D. J. Eisenstein et al., Astrophys. J. 633, 560 (2005)

CREDIT: WMAP & SDSS websites

bao method
BAO method
  • The comoving sizes of cosmological object [standard ruler] of feature at redshift z
  • in line-of-sight and transver directions
  • observed sizes
  • Two-point correlation function
updated data sets 13 1 8 2 11 ohd 2 bao
Updated data sets: 13=[1+8+2] 11 [OHD] + 2 [BAO]
  • 1. Ma Cong, Zhang Tong-Jie [arXiv:1007.3787] ApJ, 730:74 (8pp), 2011
  • 2. Zhang, Tong-Jie; Ma, Cong; Lan, Tian Hindawi Publishing Corp. Hindawi Publishing Corporation

Advances in Astronomy Volume 2010, Article ID 184284, 14 pages[eprint arXiv:1010.1307]

ze long yi tong jie zhang modern physics letters a 22 41 53 2007
Ze-Long,yi, Tong-Jie Zhang, Modern Physics letters A, 22,41-53(2007)

( arXiv:astro-ph/0605596)


3 gw method standard siren
3. GW method-Standard siren[汽笛]
  • SN or Gamma ray burst [GRB]—electromagnetic wave--standard candle [gamma-ray bursts]
  • Compact-binary object-- continuous GW— determine luminosity distance to the binaries with a high precision

standard siren

future space based gravitational wave detectors
Future space-based gravitational wave detectors
  • Such as DECI-hertz Interferometer Gravitational-wave Observatory (DECIGO) and Big-Bang Observer (BBO)
  • 1. sensitive to GW in 0.1-1Hz band
  • 2. detect GW sources

[1]. Cosmological GW background during Inflation

[2]. Mergers of an intermediate-mass black hole

[3]. A large number of(10^6) neutron star (NS) binaries: cosmological parameters can be accurately measured by DECIGO and BBO with a precision of 1%.

the advantage of the standard sirens
The advantage of the standard sirens
  • 1. the expected number of sources (NS binaries) is much larger than that of the type Ia supernovae;
  • 2. the sources are distributed deeply enough at higher redshifts.
two questions
Two Questions
  • 1. Can future observational determinations of the Hubble

parameter be used as a viable alternative to current SN Ia data?

  • 2. If so, how many more data points need?
  • Answer via an exploratory, statistical approach with simulated data
  • (1) simulated H(z) data sets;
  • (2) an “evaluation” model;
  • (3) a well-defined “figure of merit” (FoM).
data set simulation
Data set simulation

Error simulation

  • Upper line:σ+ = 16.87 z + 10.48,
  • Lower line:σ− = 4.41 z + 7.25
  • Midline:σ0 = 10.64 z + 8.86
  • Error: σ (z)-Gaussian N(σ0(z), ε(z))
  • where ε(z) = (σ+−σ−)/4.

Deviation simulation

  • Hsim(z) = Hfid(z) + ΔH with σ(z)

ΔH =Hsim(z)−Hfid(z)-Gaussian N(0,σ (z))

500 realization

Each-128 data points

figure of merit fom and the degeneracy of confidence regions
Figure of Merit[FoM]and The degeneracy of confidence regions
  • FoM-the area enclosed by the contour of P(Ωm,ΩΛ| {Hi}) = exp(−Δχ2/2)Pmax, Δχ2 =6.17
  • 1. more than 60 future measurements of H(z)[z-0-2]comparable with those obtained: SN Ia ConstitutionT;
  • 2. lower the error of future H(z) measurements to 3% , ∼60 measurements [z=0.1, 1.0] achieve the same result;
  • 3. Our result furthers a conclusion of Lin et al. (2009) and Carvalho et al. (2008), that OHD plays almost the same role as that of SNIa for the joint constraints on theΛCDMmodel.
future of ohd
三、Future of OHD

1. Observational cost:

  • ConstitutionT data[Wei Hao]: a subset of the Constitution compilation, a combination of the ground-based CfA3 SN observations (Hicken et al. 2009b) and Union, a larger compilation of legacy SNe and space-based observations (Kowalski et al. 2008). The CfA3 sample alone requires 10 nights for each of the 185 SNe observed.
  • OHD: The current OHD from age-dating does not require space-based observations. Stern et al. (2010): 24 galaxy cluster containing target chronometer galaxies were obtained in only two nights using the Keck I telescope. Crawford et al. (2010): the South African Large Telescope is capable of measuring H(z) to 3% at an individual redshift in ∼180 hr.
2 increase of quality and number
2. Increase of quality and number
  • Crawford et al. (2010) analyzed the observational requirement of measuring H(z) to 3% at intermediate redshifts with age-dating.
  • The Baryon Oscillation Spectroscopic Survey (BOSS): constrainH(z) with 2% precision at z ≈ 0.3,0.6 by measuring BAO imprints in the galaxy field, and at z ≈ 2.5 using the Lyα absorption spectra of quasars. And it also could extend H(z) measurement into deeper redshift.
  • Future CMB observation programs, such as the Atacama Cosmology Telescope[ACT], may be able to identify more than 2000 passively evolving galaxies up to z ≈ 1.5 via SZ effect, and their spectra can be analyzed to yield age measurements that will yield approximately 1000 H(z) determinations with 15% error (Simon et al. 2005).
  • the OHD set alone is potentially capable of being used in place of current SNIa data sets if it is large enough.
  • Ma, Cong; Zhang, Tong-Jie, ApJ,730,74 (2011). [eprint arXiv:1007.3787]
open questions
Open questions
  • 1. 利用差分年龄观测,是否一定要用高分辨率光谱?是否可以改变数据处理方式,通过类似于LAMOST的低分辨率光谱完成?
  • 2. 星族形成、演化的模型对差分年龄有直接影响。
  • 3. 利用差分年龄定H(z), 目前没有很系统的观测specification,更没有专门化的观测计划。因此Fisher matrix的输入值还有一些不确定性。
  • 4. 21cm线,尚无高红移的直接观测。从现在到测出21cm背景的BAO、乃至测出H(z), 还有多少路要走?
  • 5. BAO用于宇宙学模型限制,特别是从BAO得到的H(z),并没有完全消除对“fiducial model”的依赖性。这一点能否更好地解决?
h z 10
  • (1). Ma, Cong; Zhang, Tong-Jie, ApJ,730,74 (2011). [eprint arXiv:1007.3787]
  • (2). Zhang, Tong-Jie; Ma, Cong; Lan, Tian, Invited paper:

Advances in Astronomy, 184284(2010)[eprint arXiv:1010.1307]

  • (3). Zhai, Zhong-Xu; Wan, Hao-Yi; Zhang, Tong-Jie

Physics Letters B, Volume 689, Issue 1, p. 8-13(2010) (eprint arXiv:1004.2599)

  • (4). Wan, Hao-Yi; Yi, Ze-Long; Zhang, Tong-Jie; Zhou, Jie

Physics Letters B, Volume 651, Issue 5-6, p. 352-356 (08/2007) (arXiv:0706.2737)

  • (5). Yi, Ze-Long; Zhang, Tong-Jie,

Modern Physics Letters A, Vol. 22, No. 1 (01/2007) 41-53 (arXiv:astro-ph/0605596)