[28] C.M. Baugh, E. Gaztañaga, G. Efstathiou, MNRAS, 274, (1995), 1049–1070. [29] C.M. Baugh, MNRAS, 280, (1996), 267–275. [30] C.M. Baugh, E. Gaztañaga, MNRAS, 280, (1996), L37–L41. [31] D.J. Baumgart, J.N. Fry, ApJ, 375, (1991), 25–34. [32] A.J. Bean, R.S. Ellis, T. Shanks, G. Efstathiou, B.A. Peterson, MNRAS, 205, (1983), 605–624. [33] R.H. Becker, R.L. White, D.J. Helf<strong>and</strong>, ApJ, 450, (1995), 559–577. [34] K. Benabed, F. Bernardeau, astro-ph/0104371, (2001) [35] C. Benoist, A. Cappi, L.N. da Costa, S. Maurogordato, F.R. Bouchet, R. Schaeffer, ApJ, 514, (1999), 563–578. [36] A.J. Benson, S. Cole, C.S. Frenk, C.M. Baugh, C.G. Lacey, MNRAS, 311, (2000), 793–808. [37] A.J. Benson, MNRAS, 325, (2001), 1039–1044. [38] A.A. Berlind, V.K. Narayanan, D.H. Weinberg, ApJ, 549, (2001), 688–701. [39] A.A. Berlind, D.H. Weinberg, astro-ph/0109001, (2001) [40] F. Bernardeau, R. Schaeffer, A&A, 250, (1991), 23–42. [41] F. Bernardeau, R. Schaeffer, A&A, 255, (1992), 1–25. [42] F. Bernardeau, ApJ, 390, (1992), L61–L64. [43] F. Bernardeau, ApJ, 392, (1992), 1–14. [44] F. Bernardeau, A&A, 291, (1994), 697–712. [45] F. Bernardeau, ApJ, 427, (1994), 51–71. [46] F. Bernardeau, ApJ, 433, (1994), 1–18. [47] F. Bernardeau, T.P. Singh, B. Banerjee, S.M. Chitre, MNRAS, 269, (1994), 947–952. [48] F. Bernardeau, A&A, 301, (1995), 309–317. [49] F. Bernardeau, L. K<strong>of</strong>man, ApJ, 443, (1995), 479–498. [50] F. Bernardeau, R. Juszkiewicz, A. Dekel, F.R. Bouchet, MNRAS, 274, (1995), 20–26. [51] F. Bernardeau, A&A, 312, (1996), 11–23. [52] F. Bernardeau, R. Van De Weygaert, MNRAS, 279, (1996), 693–711. [53] F. Bernardeau, L. Van Waerbeke, Y. Mellier, A&A, 322, (1997), 1–18. 282
[54] F. Bernardeau, R. Van De Weygaert, E. Hivon, F.R. Bouchet, MNRAS, 290, (1997), 566–576. [55] F. Bernardeau, A&A, 338, (1998), 375–382. [56] F. Bernardeau, M.J. Chodorowski, E.L. ̷Lokas, R. Stompor, A. Kudlicki, MNRAS, 309, (1999), 543–555. [57] F. Bernardeau, R. Schaeffer, A&A, 349, (1999), 697–728. [58] F. Bernardeau, P. Valageas, A&A, 364, (2000), 1–16. [59] G.M. Bernstein, ApJ, 424, (1994), 569–577. [60] E. Bertschinger, ApJS, 58, (1985), 39–66. [61] E. Bertschinger, in New Insights into <strong>the</strong> <strong>Universe</strong>, ed. V.J. Martinez, M. Portilla, D. Saez (Berlin: Springer), 1992, 65-126. [62] E. Bertschinger, B. Jain, ApJ, 431, (1994), 486–494. [63] E. Bertschinger, ARA&A, 36, (1998), 599–654. [64] E. Bertschinger, astro-ph/0103301, (2001) [65] P. Binetruy, C. Deffayet, E. Dudas, P. Ramond, Phys. Lett., B441, (1998), 163–172. [66] P. Binetruy, C. Deffayet, P. Peter, Phys. Lett., B441, (1998), 52–59. [67] J.J. Binney, N.J. Dowrick, A.J. Fisher, M.E.J. Newman, The Theory <strong>of</strong> Critical Phenomena (Oxford University Press, 1992). [68] A. Blanchard, J.-M. Alimi, A&A, 203, (1988), L1–L4. [69] R.D. Bl<strong>and</strong>ford, Q. Jl. R. Astr. Soc., 31, (1990), 305-331. [70] R.D. Bl<strong>and</strong>ford, A.B. Saust, T.G. Brainerd, J.V. Villumsen, MNRAS, 251, (1991), 600–627. [71] M.R. Blanton, ApJ, 544, (2000), 63–80. [72] M.R. Blanton, R. Cen, J. Ostriker, M. Strauss, ApJ, 522, (1999), 590–603. [73] M.R. Blanton, R. Cen, J. Ostriker, M. Strauss, M. Tegmark, ApJ, 531, (2000), 1–16. [74] M.R. Blanton, R.H. Lupton, F. Miller Maley, N. Young, I. Zehavi, J. Loveday, (2001), astro-ph/0105535 [75] G.R. Blumenthal, S.M. Faber, J.R. Primack, M.J. Rees, Nature, 311, (1984), 517–525. [76] J.R. Bond, G. Efstathiou, ApJ, 285, (1984), L45–L48. 283
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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
- 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 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
- 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: References [1] S.J. Aarseth, E.L. T
- Page 285 and 286: [100] A. Buchalter, M. Kamionkowski
- Page 287 and 288: [150] S. Colombi, F.R. Bouchet, L.
- Page 289 and 290: [196] G. Efstathiou, in Cosmology a
- Page 291 and 292: [245] A. Gangui, Phys. Rev. D, 62,
- Page 293 and 294: [299] A.J.S. Hamilton, M. Tegmark,
- Page 295 and 296: [352] R. Jeannerot, Phys. Rev. D, 5
- Page 297 and 298: [399] A.R. Liddle, D.H. Lyth, Phys.
- Page 299 and 300: [448] P. McDonald, J. Miralda-Escud
- Page 301 and 302: [497] J.A. Peacock, S. Cole, P. Nor
- Page 303 and 304: [547] R.F. Sanford, 1917, Lick Obse
- Page 305 and 306: [597] M. Snethlage, Metrica, 49, (1
- Page 307 and 308: [644] A.N. Taylor, P.I.R. Watts, MN
- Page 309: [692] M.B. Wise, in The Early Unive