Large-Scale Structure of the Universe and Cosmological ...

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Fig. 49. The Sp parameters for p = 3,4,5 (from bottom to top) in redshift space for ΛCDM with σ8 = 0.9 as a function of smoothing scale R. Square symbols denote measurements in real space N-body simulations, whereas triangles correspond to redshift-space values, assuming the plane-parallel approximation. and that bias is linear, scale and time independent, concludes that the best prospects for measuring cosmological distortions in upcoming surveys is given by the LRG (luminous red galaxy) sample of the SDSS. This sample of about 100,000 galaxies seems to give a good balance between probing structure down to ‘high’ redshift (z ∼ 0.5) and having a large enough number density so that shot noise is not a limiting factor. Analysis of redshift and cosmological distortions gives a joint 3-σ uncertainty on ΩΛ and Ωm of about 15%, assuming ΩΛ = 0.7 and Ωm = 0.3 as the fiducial model. Other surveys such as the quasar samples in 2dFGRS and SDSS, are predicted to give less stringent constraints due to the sparse sampling [444]. Applications of cosmological distortions to the case of the Lyman-α forest have been proposed in the literature [329,448]. In this case, the distortions are computed by comparing correlations along the line of sight to those by crosscorrelating line of sights of nearby quasars. These studies conclude that with only about 25 pairs of quasars at angular separations of < ∼ 2 ′ −3 ′ it is possible to distinguish an open model from a flat cosmological constant dominated model (with the same Ωm = 0.3) at the 4-σ level. These results, however, assume a linear description of redshift distortions. More recent analysis using numerical simulations [449] suggests that with 13(θ/1 ′ ) 2 pairs at separation less than θ, and including separations < 10 ′ , a measurement to 5% can be made if simulations can predict the redshift-space anisotropy with 5% accuracy, or to 10% if the anisotropy must be measured from the data. Finally, we should mention the effect of clustering evolution along the line of sight, due to observation along the light cone. Estimates of this effect show 218
that for wide surveys such as 2dFGRS and SDSS it amounts to about 10% in the power spectrum and higher-order statistics, while it becomes significantly larger of course for deep surveys, see e.g. [439,283]. 219
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arXiv:astro-ph/0112551v1 27 Dec 200
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4.1.1 Emergence of Non-Gaussianity
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6.11.1 Maximum Likelihood Estimates
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1 Introduction and Notation Underst
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with N-point functions, whereas Cha
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Table 3 Notation for the Cosmic Fie
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2 Dynamics of Gravitational Instabi
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In the following we will only use c
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∂u(x, τ) + H(τ) u(x, τ) = −
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Eq. (17) we can write the vorticity
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θn(k) = d 3 q1 . . . d 3 qn δD(k
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2.4.3 Cosmology Dependence of Non-L
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approximation f(Ωm, ΩΛ) = Ω3
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The somewhat complicated expression
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where Φ denotes the gravitational
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or more precisely D2(τ) ≈ − 3
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ever turning around, washing out st
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2.9.2 Direct Summation Also known a
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(e.g., [314,532]). Finally, it is w
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such initial conditions are likely
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3.2.1 Statistical Homogeneity and I
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δ 1 δ δ 2 3 c = δ1 c = 00000 11
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3.2.5 Probabilities and Correlation
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3.3.3 Generating Functions It is co
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values of y are then also of the or
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4 From Dynamics to Statistics: N-Po
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Figures 5 and 6 show the tree diagr
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e approximated by a fitting functio
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Fig. 10. The tree-level three-point
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4 2 0 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0
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n P13/(πA 2 a 4 ) P22/(πA 2 a 4 )
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Fig. 13. The power spectrum for n =
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where: B222 ≡ 8 d 3 qPL(q, τ)F
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Fig. 16. The left panel shows the o
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them in Sect. 5.6. It is worth emph
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Fig. 17. The reduced bispectrum ˜
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(1) There are no characteristic tim
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velocity exactly cancels the Hubble
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A simple generalization of this arg
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growth factor has been written as D
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function in the stable clustering l
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S sat 4 (n) = 16 Qsat 4 (n) = 8 54
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For the reasons discussed in Sect.
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δ δ Evolution of an initially und
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obtained by expansion about Ωm =
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y the orthogonality relation betwee
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σ = 2 ; ν σ = ; 4 2 ν σ = 6 3
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(that plays a role similar to the v
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Fig. 26. The predicted Sp parameter
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Table 6 Tree-level and one-loop cor
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expressed in terms of the linear de
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give to non-Gaussian initial condit
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+ −4 + 8 3 SG 3 − 1 S 6 G 2 3
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the initial conditions. In Sect. 2.
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Fig. 30. The ratio of the tree-leve
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5.8 The Density PDF Up to now, we h
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Fig. 32. Comparison between predict
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9 5 p(δ) = 3/2 4π Ns(1 + δ) 3 σ
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Table 10 Parameters of the singular
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5.10.2 The Shape of the PDF The abo
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Fig. 35. Example of a joint PDF of
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Table 11 The coefficients a1,... ,a
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originally in previous work in the
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Table 12 Parameters used in fit (35
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6 From Theory to Observations: Esti
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the size of the catalog and optimiz
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The cosmic error is most useful whe
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expectation number ¯ N = ¯ngv, P
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1 〈δn(k1)δn(k2)δn(k3)〉 = N2
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catalog, the latter being equivalen
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size. In this regime, where ξ(r) i
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The expressions (395) and (400) can
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The techniques developed to measure
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At smaller scales, in the regime k
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Fig. 38. The top panel shows the me
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If ¯ng is determined with arbitrar
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Factorial moments thus verify Fk =
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To second order the cosmic bias [Eq
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The finite-volume error comes from
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6.7.5 Cosmic Error and Cosmic Bias
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factorial moment correlators [620]
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The generalization of Eq. (422) rea
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in [152]. Similarly to Eq. (472), t
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Page 169 and 170: From this simple result, we see tha
Page 171 and 172: Fig. 41. The cosmic distribution fu
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Page 175 and 176: 6.11.2 Quadratic Estimators In real
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Page 179 and 180: 6.12 Measurements in N-Body Simulat
Page 181 and 182: 7 Applications to Observations 7.1
Page 183 and 184: properties of the matter distributi
Page 185 and 186: deterministic bias results hold for
Page 187 and 188: effects due to the gravitational dy
Page 189 and 190: 0000 1111 0000 1111 ϕ (y)= 0000 11
Page 191 and 192: where the volume V = 4πR3 /3 is re
Page 193 and 194: in Sect. 7.1.3, Eq. (555), plus Eqs
Page 195 and 196: In the following we first review th
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Page 199 and 200: Table 13 Projection factors for dif
Page 201 and 202: Note that the rp coefficients are v
Page 203 and 204: Fig. 47. Tree-level PT predictions
Page 205 and 206: 7.3 Weak Gravitational Lensing The
Page 207 and 208: elation (598) is then entirely dime
Page 209 and 210: 7.4 Redshift Distortions In order t
Page 211 and 212: where [δD]n ≡ δD(k − k1 −
Page 213 and 214: proximation. In fact, Eq. (616) is
Page 215 and 216: Fig. 48. The left panel shows the b
Page 217: They obtained analogous results to
Page 221 and 222: Machine, [374]) and COSMOS [421] mi
Page 223 and 224: Table 14 Angular Catalogs. The firs
Page 225 and 226: The DeepRange Catalog ([530] 1998)
Page 227 and 228: Fig. 50. The two-point angular corr
Page 229 and 230: Fig. 51. The APM 3D power spectrum
Page 231 and 232: linearization first done in [289] a
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Page 235 and 236: and Rb = 4.3 ± 1.2 [226]. These re
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Page 239 and 240: Table 16 The reduced skewness and k
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Page 243 and 244: the near future. An early applicati
Page 245 and 246: The Stromlo-APM redshift survey ([4
Page 247 and 248: A recent linear analysis of the LCR
Page 249 and 250: at the non-linear scale, and no sig
Page 251 and 252: Fig. 57. The redshift-space reduced
Page 253 and 254: Table 19 Some measurements of S3 an
Page 255 and 256: Fig. 60. The redshift-space skewnes
Page 257 and 258: such as the abundance of massive cl
Page 259 and 260: the weakly non-linear regime is qui
Page 261 and 262: the mock catalogs. The resulting 3D
Page 263 and 264: few technical issues that need more
Page 265 and 266: A The Spherical Collapse Dynamics T
Page 267 and 268: More specifically we define ϕ(y) a
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∞ (−τ1) τ2 =ξ y1 νp p=1 p
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This result writes as a kind of com
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E PDF Construction from Cumulant Ge
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E.3 Approximate Forms for P(ρ) whe
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A simple change of variable, t 1−
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It is then easy to calculate cross-
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References [1] S.J. Aarseth, E.L. T
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[54] F. Bernardeau, R. Van De Weyga
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[150] S. Colombi, F.R. Bouchet, L.
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[196] G. Efstathiou, in Cosmology a
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[245] A. Gangui, Phys. Rev. D, 62,
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[299] A.J.S. Hamilton, M. Tegmark,
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[352] R. Jeannerot, Phys. Rev. D, 5
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[399] A.R. Liddle, D.H. Lyth, Phys.
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[448] P. McDonald, J. Miralda-Escud
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[547] R.F. Sanford, 1917, Lick Obse
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[644] A.N. Taylor, P.I.R. Watts, MN
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[692] M.B. Wise, in The Early Unive
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