[217] K.B. Fisher, M. Davis, M.A. Strauss, A. Yahil, J.P. Huchra, MNRAS, 267, (1994), 927–948. [218] K.B. Fisher, J.P. Huchra, M.A. Strauss, M. Davis, A. Yahil, D. Schlegel, ApJS, 100, (1995), 69–103. [219] K.B. Fisher, ApJ, 448, (1995), 494–499. [220] K.B. Fisher, A. Nusser, ApJ, 279, (1996), L1–L5. [221] R. Fong, D. Hale-Sutton, T. Shanks MNRAS, 257, (1992), 650–658. [222] P. Fosalba, E. Gaztañaga, MNRAS, 301, (1998), 503–523. [223] P. Fosalba, E. Gaztañaga, MNRAS, 301, (1998), 535–546. [224] J.A. Frieman, E. Gaztañaga, ApJ, 425, (1994), 392–402. [225] J.A. Frieman, E. Gaztañaga, ApJ, 521, (1999), L83–L86. [226] J.N. Fry, P.J.E. Peebles, ApJ, 221, (1978), 19–33. [227] J.N. Fry, P.J.E. Peebles, ApJ, 238, (1980), 785–792. [228] J.N. Fry, ApJ, 262, (1982), 424–431. [229] J.N. Fry, M. Seldner, ApJ, 259, (1982), 474–481. [230] J.N. Fry, ApJ, 267, (1983), 483–487. [231] J.N. Fry, ApJ, 277, (1984), L5–L8. [232] J.N. Fry, ApJ, 279, (1984), 499–510. [233] J.N. Fry, ApJ, 289, (1985), 10–17. [234] J.N. Fry, A.L. Melott, S.F. Sh<strong>and</strong>arin, ApJ, 412, (1993), 504–512. [235] J.N. Fry, E. Gaztañaga, ApJ, 413, (1993), 447–452. [236] J.N. Fry, Phys. Rev. Lett., 73, (1994), 215–219. [237] J. N. Fry, ApJ, 421, (1994), 21–26. [238] J.N. Fry, R.J. Scherrer, ApJ, 429, (1994), 36–42. [239] J.N. Fry, E. Gaztañaga, ApJ, 425, (1994), 1–13. [240] J.N. Fry, A.L. Melott, S.F. Sh<strong>and</strong>arin, MNRAS, 274, (1995), 745–754. [241] J.N. Fry, ApJ, 461, (1996), L65–L67. [242] J.N. Fry, D. Thomas, ApJ, 524, (1999), 591–602. [243] T. Fukushige, J. Makino, ApJ, 477, (1997), L9–L12. [244] T. Fukushige, Y. Suto, ApJ, 557, (2001), L11–L14. 290
[245] A. Gangui, Phys. Rev. D, 62, (2000), 103004. [246] E. Gaztañaga, ApJ, 398, (1992), L17–L20. [247] E. Gaztañaga, J. ’I. Yokoyama, ApJ, 403, (1993), 450–465. [248] E. Gaztañaga, J.A. Frieman, ApJ, 437, (1994), L13–L16. [249] E. Gaztañaga, MNRAS, 268, (1994), 913–924. [250] E. Gaztañaga, ApJ, 454, (1995), 561–572. [251] E. Gaztañaga, C.M. Baugh, MNRAS, 273, (1995), 1P–6P. [252] E. Gaztañaga, P. Mähönen, ApJ, 462, (1996), L1–L4. [253] E. Gaztañaga, C.M. Baugh, MNRAS, 294, (1998), 229–244. [254] E. Gaztañaga, F. Bernardeau, A&A, 331, (1998), 829–837. [255] E. Gaztañaga, P. Fosalba, MNRAS, 301, (1998), 524–534. [256] E. Gaztañaga, R.A.C. Cr<strong>of</strong>t, MNRAS, 309, (1999), 885–904. [257] E. Gaztañaga, G.B. Dalton, MNRAS, 312, (2000), 417–428. [258] E. Gaztañaga, P. Fosalba, E. Elizalde, ApJ, 539, (2000), 522–531. [259] E. Gaztanaga, A. Lobo, ApJ, 548, (2001), 47–59. [260] E. Gaztanaga, R. Juszkiewicz, ApJ, 558, (2001), L1–L4. [261] E. Gaztanaga, astro-ph/0106379, (2001) [262] E. Gaztanaga, astro-ph/0110126, (2001) [263] E. Gaztañaga, P. Fosalba, R.A.C. Cr<strong>of</strong>t, (2001), astro-ph/0107523 [264] S. Gelato, D.F. Chern<strong>of</strong>f, I. Wasserman, ApJ, 480, (1997), 115–131. [265] M.J. Geller, M.J. Kurtz, V. de Lapparent, ApJ, 287, (1984), L55–L58. [266] M.J. Geller, M.J. Kurtz, G. Wegner, J.R. Thorstensen, D.G. Fabricant, R.O. Marzke, J.P. Huchra, R.E. Schild, E.E. Falco, AJ, 114, (1997), 2205–2211. [267] S. Ghigna, S.A. Bonometto, L. Guzzo, R. Giovanelli, M.P. Haynes, A. Klypin, J.R. Primack, ApJ, 463, (1996), 395–403. [268] R. Giovanelli, M.P. Haynes, ARA&A, 29, (1991), 499–541. [269] N.Y. Gnedin, ApJS, 97, (1995), 231–257. [270] M.H. Gor<strong>of</strong>f, B. Grinstein, S.-J. Rey, M.B. Wise, ApJ, 311, (1986), 6–14. [271] J.R. Gott, M.J. Rees, A&A, 45, (1975), 365–376. [272] J.R. Gott, E.L. Turner, ApJ, 232, (1979), L79–L81. 291
- Page 1 and 2:
arXiv:astro-ph/0112551v1 27 Dec 200
- Page 3 and 4:
4.1.1 Emergence of Non-Gaussianity
- Page 5 and 6:
6.11.1 Maximum Likelihood Estimates
- Page 7 and 8:
1 Introduction and Notation Underst
- Page 9 and 10:
with N-point functions, whereas Cha
- Page 11 and 12:
Table 3 Notation for the Cosmic Fie
- Page 13 and 14:
2 Dynamics of Gravitational Instabi
- Page 15 and 16:
In the following we will only use c
- Page 17 and 18:
∂u(x, τ) + H(τ) u(x, τ) = −
- Page 19 and 20:
Eq. (17) we can write the vorticity
- Page 21 and 22:
θn(k) = d 3 q1 . . . d 3 qn δD(k
- Page 23 and 24:
2.4.3 Cosmology Dependence of Non-L
- Page 25 and 26:
approximation f(Ωm, ΩΛ) = Ω3
- Page 27 and 28:
The somewhat complicated expression
- Page 29 and 30:
where Φ denotes the gravitational
- Page 31 and 32:
or more precisely D2(τ) ≈ − 3
- Page 33 and 34:
ever turning around, washing out st
- Page 35 and 36:
2.9.2 Direct Summation Also known a
- Page 37 and 38:
(e.g., [314,532]). Finally, it is w
- Page 39 and 40:
such initial conditions are likely
- Page 41 and 42:
3.2.1 Statistical Homogeneity and I
- Page 43 and 44:
δ 1 δ δ 2 3 c = δ1 c = 00000 11
- Page 45 and 46:
3.2.5 Probabilities and Correlation
- Page 47 and 48:
3.3.3 Generating Functions It is co
- Page 49 and 50:
values of y are then also of the or
- Page 51 and 52:
4 From Dynamics to Statistics: N-Po
- Page 53 and 54:
Figures 5 and 6 show the tree diagr
- Page 55 and 56:
e approximated by a fitting functio
- Page 57 and 58:
Fig. 10. The tree-level three-point
- Page 59 and 60:
4 2 0 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0
- Page 61 and 62:
n P13/(πA 2 a 4 ) P22/(πA 2 a 4 )
- Page 63 and 64:
Fig. 13. The power spectrum for n =
- Page 65 and 66:
where: B222 ≡ 8 d 3 qPL(q, τ)F
- Page 67 and 68:
Fig. 16. The left panel shows the o
- Page 69 and 70:
them in Sect. 5.6. It is worth emph
- Page 71 and 72:
Fig. 17. The reduced bispectrum ˜
- Page 73 and 74:
(1) There are no characteristic tim
- Page 75 and 76:
velocity exactly cancels the Hubble
- Page 77 and 78:
A simple generalization of this arg
- Page 79 and 80:
growth factor has been written as D
- Page 81 and 82:
function in the stable clustering l
- Page 83 and 84:
S sat 4 (n) = 16 Qsat 4 (n) = 8 54
- Page 85 and 86:
For the reasons discussed in Sect.
- Page 87 and 88:
δ δ Evolution of an initially und
- Page 89 and 90:
obtained by expansion about Ωm =
- Page 91 and 92:
y the orthogonality relation betwee
- Page 93 and 94:
σ = 2 ; ν σ = ; 4 2 ν σ = 6 3
- Page 95 and 96:
(that plays a role similar to the v
- Page 97 and 98:
Fig. 26. The predicted Sp parameter
- Page 99 and 100:
Table 6 Tree-level and one-loop cor
- Page 101 and 102:
expressed in terms of the linear de
- Page 103 and 104:
give to non-Gaussian initial condit
- Page 105 and 106:
+ −4 + 8 3 SG 3 − 1 S 6 G 2 3
- Page 107 and 108:
the initial conditions. In Sect. 2.
- Page 109 and 110:
Fig. 30. The ratio of the tree-leve
- Page 111 and 112:
5.8 The Density PDF Up to now, we h
- Page 113 and 114:
Fig. 32. Comparison between predict
- Page 115 and 116:
9 5 p(δ) = 3/2 4π Ns(1 + δ) 3 σ
- Page 117 and 118:
Table 10 Parameters of the singular
- Page 119 and 120:
5.10.2 The Shape of the PDF The abo
- Page 121 and 122:
Fig. 35. Example of a joint PDF of
- Page 123 and 124:
Table 11 The coefficients a1,... ,a
- Page 125 and 126:
originally in previous work in the
- Page 127 and 128:
Table 12 Parameters used in fit (35
- Page 129 and 130:
6 From Theory to Observations: Esti
- Page 131 and 132:
the size of the catalog and optimiz
- Page 133 and 134:
The cosmic error is most useful whe
- Page 135 and 136:
expectation number ¯ N = ¯ngv, P
- Page 137 and 138:
1 〈δn(k1)δn(k2)δn(k3)〉 = N2
- Page 139 and 140:
catalog, the latter being equivalen
- Page 141 and 142:
size. In this regime, where ξ(r) i
- Page 143 and 144:
The expressions (395) and (400) can
- Page 145 and 146:
The techniques developed to measure
- Page 147 and 148:
At smaller scales, in the regime k
- Page 149 and 150:
Fig. 38. The top panel shows the me
- Page 151 and 152:
If ¯ng is determined with arbitrar
- Page 153 and 154:
Factorial moments thus verify Fk =
- Page 155 and 156:
To second order the cosmic bias [Eq
- Page 157 and 158:
The finite-volume error comes from
- Page 159 and 160:
6.7.5 Cosmic Error and Cosmic Bias
- Page 161 and 162:
factorial moment correlators [620]
- Page 163 and 164:
The generalization of Eq. (422) rea
- Page 165 and 166:
in [152]. Similarly to Eq. (472), t
- Page 167 and 168:
constrain theories with observation
- Page 169 and 170:
From this simple result, we see tha
- Page 171 and 172:
Fig. 41. The cosmic distribution fu
- Page 173 and 174:
of functions of the data ˆx. The p
- Page 175 and 176:
6.11.2 Quadratic Estimators In real
- Page 177 and 178:
is positive and compact in Fourier
- 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
- Page 197 and 198:
if the 3D correlation function is
- 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 and 218:
They obtained analogous results to
- Page 219 and 220:
that for wide surveys such as 2dFGR
- 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
- Page 233 and 234:
most of the measurements only probe
- Page 235 and 236:
and Rb = 4.3 ± 1.2 [226]. These re
- Page 237 and 238:
3 2 1 3 2 1 0 -1 10 5 0 -5 -10 0 90
- Page 239 and 240: Table 16 The reduced skewness and k
- Page 241 and 242: estimations are split in its 6 × 6
- 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
- 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
- Page 283 and 284: [54] F. Bernardeau, R. Van De Weyga
- Page 285 and 286: [100] A. Buchalter, M. Kamionkowski
- Page 287 and 288: [150] S. Colombi, F.R. Bouchet, L.
- Page 289: [196] G. Efstathiou, in Cosmology a
- 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