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

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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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constrain theories with observation
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From this simple result, we see tha
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Fig. 41. The cosmic distribution fu
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of functions of the data ˆx. The p
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6.11.2 Quadratic Estimators In real
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is positive and compact in Fourier
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6.12 Measurements in N-Body Simulat
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7 Applications to Observations 7.1
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properties of the matter distributi
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deterministic bias results hold for
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effects due to the gravitational dy
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0000 1111 0000 1111 ϕ (y)= 0000 11
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where the volume V = 4πR3 /3 is re
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in Sect. 7.1.3, Eq. (555), plus Eqs
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In the following we first review th
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if the 3D correlation function is
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Table 13 Projection factors for dif
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Note that the rp coefficients are v
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Fig. 47. Tree-level PT predictions
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7.3 Weak Gravitational Lensing The
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elation (598) is then entirely dime
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7.4 Redshift Distortions In order t
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where [δD]n ≡ δD(k − k1 −
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proximation. In fact, Eq. (616) is
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Fig. 48. The left panel shows the b
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They obtained analogous results to
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that for wide surveys such as 2dFGR
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Machine, [374]) and COSMOS [421] mi
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Table 14 Angular Catalogs. The firs
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The DeepRange Catalog ([530] 1998)
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Fig. 50. The two-point angular corr
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Fig. 51. The APM 3D power spectrum
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linearization first done in [289] a
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most of the measurements only probe
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and Rb = 4.3 ± 1.2 [226]. These re
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3 2 1 3 2 1 0 -1 10 5 0 -5 -10 0 90
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Table 16 The reduced skewness and k
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estimations are split in its 6 × 6
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the near future. An early applicati
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The Stromlo-APM redshift survey ([4
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A recent linear analysis of the LCR
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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
Page 269 and 270: ∞ (−τ1) τ2 =ξ y1 νp p=1 p
Page 271 and 272: This result writes as a kind of com
Page 273 and 274: E PDF Construction from Cumulant Ge
Page 275 and 276: E.3 Approximate Forms for P(ρ) whe
Page 277 and 278: A simple change of variable, t 1−
Page 279 and 280: It is then easy to calculate cross-
Page 281 and 282: References [1] S.J. Aarseth, E.L. T
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Page 307 and 308: [644] A.N. Taylor, P.I.R. Watts, MN
Page 309: [692] M.B. Wise, in The Early Unive
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