Measuring our Universe from Galaxy Redshift Surveys

Abstract

Galaxy redshift surveys have achieved significant progress over the last couple of decades. Those surveys tell us in the most straightforward way what our local Universe looks like. While the galaxy distribution traces the bright side of the Universe, detailed quantitative analyses of the data have even revealed the dark side of the Universe dominated by non-baryonic dark matter as well as more mysterious dark energy (or Einstein's cosmological constant). We describe several methodologies of using galaxy redshift surveys as cosmological probes, and then summarize the recent results from the existing surveys. Finally we present our views on the future of redshift surveys in the era of precision cosmology.

Figure 1

Evolution of the cosmic scale factor as a function of H₀(t − t₀). The present value of the scale factor a₀ is set to unity; solid line: (Ω_m, Ω_Λ) = (0.3, 1.7), dotted line: (0.3, 0.7), dot-dashed line: (0.3, 0.0), long dashed line: (1.0, 0.0), short dashed line: (3.0, 0.0).

Figure 2

Linear growth rate of density fluctuations.

Figure 3

One-point PDFs in CDM models with Gaussian (left panels) and top-hat (right panels) smoothing windows: R = 2 h⁻¹ Mpc (cyan), 6 h⁻¹ Mpc (red), and 18 h⁻¹ Mpc (green). The solid and long-dashed lines represent the log-normal PDF adopting σ_nl calculated directly from the simulations and estimated from the nonlinear fitting formula of [67], respectively. (Figure taken from [40].)

Figure 4

Isodensity surfaces of dark matter distribution from N-body simulation: LCDM in (100 h⁻¹ Mpc)³ at ν = −1.0 (upper left panel), ν = 0.0 (upper right panel), ν = 1.0 (lower left panel), and ν = 1.7 (lower right panel). (Figure taken from [54].)

Figure 5

Top-view of distribution of objects at z = 0 in real (left panels) and redshift (right panels) spaces around the fiducial observer at the center: dark matter particles (top panels), peaks with ν > 2 (middle panels), and halos with M > 1.3 × 10¹²M_⊙ (bottom panels) in the LCDM model. The thickness of those slices is 15 h⁻¹ Mpc. (Figure taken from [86].)

Figure 6

Same as Figure 5, but at z = 2.2. (Figure taken from [86].)

Figure 7

Auto- and cross-correlation functions of dark matter and peaks in SCDM (left panels), LCDM (middle panels), and OCDM (right panels) for (a) z = 0 (upper panels) and (b) z = 2.2 (lower panels). Different symbols indicate the results in real space (open squares for ν > 3, filled triangles for ν > 2, open circles for ν > 1, and crosses for dark matter), while different curves indicate those in redshift space (dashed for ν > 3, dot-dashed for ν > 2, solid for ν > 1, and dotted for dark matter). (Figure taken from [86].)

Figure 8

Same as Figure 7, but for a halo model, again for (a) z = 0 (upper panels) and (b) z = 2.2 (lower panels): Open squares and dashed lines for M > 10¹³ h⁻¹M_⊙, filled triangles and dot-dashed lines for M > 5 × 10¹² h⁻¹M_⊙, open circles and solid lines for M > 2 × 10¹² h⁻¹M_⊙, and crosses and dotted lines for dark matter. For the SCDM model, we only plot the correlation functions with M_th = 5 × 10¹² h⁻¹M_⊙ and M_th = 10¹³ h⁻¹M_⊙. (Figure taken from [86].)

Figure 9

Distribution of gas particles (upper right panel), dark matter particles (upper left panel), galaxies (lower right panel), and dark halos (lower left panel) in the volume of a 75h⁻¹ × 75 h⁻¹ × 30 h⁻¹ Mpc³ model at z = 0. (Figure taken from [103].)

Figure 10

Snapshots of the most massive cluster (M ≃ 8 × 10¹⁴M_⊙) in the simulation at z = 0. Upper left panel: dark matter; upper right panel: gas; lower left panel: DM cores; lower right panel: cold gas. The circles in the lower panels indicate the positions of galaxies identified according to our criteria. The comoving size of the box is 6.25 h⁻¹ Mpc per side. (Figure taken from [103].)

Figure 11

Joint probability distributions of overdensity fields for dark halos and galaxies with dark matter overdensity smoothed over R_s = 12 h⁻¹ Mpc at redshift z = 0, 1, and 2. Solid lines indicate the conditional mean for each object. Dashed lines in each panel depict the theoretical prediction of conditional mean by Taruya and Suto [87]. (Figure taken from [103].)

Figure 12

Two-point correlation functions of dark matter, galaxies, and dark halos from cosmological hydrodynamical simulations. (Figure taken from [103].)

Figure 13

Two-point correlation functions for the old and young populations of galaxies at z = 0 as well as that of the dark matter distribution. The profiles of bias parameters b_ξ(r) for both of the two populations are also shown in the lower panel. (Figure taken from [103].)

Figure 14

Mass two-point correlation functions on the light-cone for particles with redshift-dependent selection functions in the SCDM model, for z < 0.4 (upper panels) and 0.2 < z < 2.0 (lower panels). Left panels: with selection function whose shape is the same as that of the B-band magnitude limit of 19 for galaxies (upper) and 21 for QSOs (lower); right panels: randomly selected N ∼ 10⁴ particles from the particles in the results from the left panels. (Figure taken from [28].)

Figure 15

Same as Figure 14 but for the Λ-CDM model. (Figure taken from [28].)

Figure 16

Two-dimensional power spectra in cosmological redshift space at z = 2.2. (Figure taken from [46].)

Figure 17

The confidence contours on the Ω_m-Ω_Λ plane from the χ²-analysis of the monopole and quadrupole moments ofthe power spectrum in the cosmological redshift space at z = 2.2. We randomly selected N = 5 × 10³ (upper panels), N = 5 × 10⁴ (middle panels), and N = 5 × 10⁵ (lower panels) particles from N-body simulation. The value of σ₈ is adopted from the cluster abundance. (Figure taken from [46].)

Figure 18

Light-cone and cosmological redshift-space distortion effects on angle-averaged power spectra. (Figure taken from [84].)

Figure 19

Same as Figure 18 on angle-averaged two-point correlation functions. (Figure taken from [84].)

Figure 20

The 2dFGRS fields (small circles) superimposed on the APM catalogue area (dotted outlines of Sky Survey plates).

Figure 21

The distribution of 63,000 2dFGRS galaxies in the NGP (left panel) and SGP (right panel) strips.

Figure 22

3D redshift-space map centered on us, and its projection on the celestial sphere of SDSS galaxy subset, including the three main regions. (Figure taken from [32].)

Figure 23

Redshift slices of SDSS galaxy data around the equatorial plane. The redshift limits and the thickness of the planes are z < 0.05 and 10 h⁻¹ Mpc (upper panel), z < 0.1 and 15 h⁻¹ Mpc (middle panel), and z < 0.2 and 20 h⁻¹ Mpc (lower panel). The size of points has been adjusted. Note that the data for the Southern part are sparser than those for the Northern part, especially for thick slices. (Figure taken from [32].)

Figure 24

The power spectrum of the 2dFGRS. The points with error bars show the measured 2dFGRS power spectrum measurements in redshift space, convolved with the window function. Also plotted are linear CDM models with neutrino contribution of Ω_ν = 0, Ω_ν = 0.01, and Ω_ν = 0.05 (bottom to top lines). The other parameters are fixed to the concordance model. The good fit of the linear theory power spectrum at k > 0.15 h Mpc⁻¹ is due to a conspiracy between the non-linear gravitational growth and the finger-of-God smearing [72]. (Figure taken from [20].)

Figure 25

The variation of the galaxy biasing parameter with luminosity, relative to an L_* galaxy for the full sample and for subsamples of early and late spectra types. (Figure taken from [61].)

Figure 26

The two point correlation function ξ(σ, π) plotted for passively (left panel) and actively (right panel) star-forming galaxies. The line contours levels show the best-fitting model. (Figure taken from [45].)

Figure 27

The correlation function for early and late spectral types. The solid lines show best-fitting models, whereas the dashes lines are extrapolations of these lines. (Figure taken from [45].)

Figure 28

The SDSS (EDR) projected correlation function for blue (squares), red (triangles) and the full sample, with best-fitting models over the range 0.1 < r_p < 16 h⁻¹ Mpc (upper panel), and the SDSS (EDR) projected correlation function for three volume-limited samples, with absolute magnitude and redshift ranges as indicated and best-fitting power-law models (lower panel). (Figure taken from [104].)

Figure 29

Dimensionless amplitude of the three-point correlation functions of SDSS galaxies in redshift space. The galaxies are classified according to their colors; all galaxies in open circles, red galaxies in solid triangles, and blue galaxies in crosses. (Figure taken from [39].)

Figure 30

Same as Figure 29, but for the inverse of the biasing parameter defined through the two-point correlation functions. (Figure taken from [39].)

Figure 31

MFs as a function of ν_f for R_G = 5 h⁻¹ Mpc for SDSS data. Averaged MFs of the mock samples are plotted for LCDM (solid lines) and SCDM (long dashed lines). Gaussian model predictions (see Equations (112, 113, 114, 115)) are also plotted with short dashed lines. The results favor the LCDM model with random-Gaussian initial conditions. (Figure taken from [32].)