Quantifying large-scale structure 73redshift. Thus, withξ∝r−γ, we obtain the comoving evolution
ξ(r,z)∝( 1 +z)γ−^3 (nonlinear).Since the observedγ 1 .8, this implies slower evolution than is expected in the
linear regime:
ξ(r,z)∝( 1 +z)−^2 g() (linear).
This argument does not so far give a relation between the nonlinear slopeγand
the indexnof the linear spectrum. However, the linear and nonlinear regimes
match at the scale of quasilinearity, i.e.ξ(r 0 ) =1; each regime must make
the same prediction for how this break point evolves. The linear and nonlinear
predictions for the evolution ofr 0 are, respectively,r 0 ∝( 1 +z)−^2 /(n+^3 )and
r 0 ∝( 1 +z)−(^3 −γ)/γ,sothatγ=( 3 n+ 9 )/(n+ 5 ). In terms of an effective index
γ= 3 +nNL, this becomes
nNL=−6
5 +n.
The power spectrum resulting from power-law initial conditions will evolve self-
similarly with this index. Note the narrow range predicted:− 2 <nNL<−1for
− 2 <n<+1, with ann=−2 spectrum having the same shape in both linear
and nonlinear regimes.
For many years it was thought that only these limiting cases of extreme
linearity or nonlinearity could be dealt with analytically, but in a marvelous
piece of alchemy, Hamiltonet al(1991; HKLM) suggested a general way of
understanding the linear↔nonlinear mapping. This initial idea was extended
into a workable practical scheme by Peacock and Dodds (1996), allowing the
effects of nonlinear evolution to be calculated to a few per cent accuracy for a
wide class of spectra.
Indications from the angular clustering of faint galaxies (Efstathiouet al
1991) and directly from redshift surveys (Le F`evreet al1996) are that the
observed clustering of galaxies evolves at about the linear-theory rate forz. 0 .5,
rather more rapidly than the scaling solution would indicate. However, any
interpretation of such data needs to assume that galaxies are unbiased tracers of
the mass, whereas the observed high amplitude of clustering of quasars atz 1
(r 0 7 h−^1 Mpc; see Shankset al1987, Shanks and Boyle 1994) were an early
warning that some high-redshift objects had clustering that is apparently not due
to gravity alone. When it eventually became possible to measure correlations of
normal galaxies atz&1 directly, a similar effect was found, with the comoving
strength of clustering being comparable to its value atz=0 (e.g. Adelbergeret
al1998, Carlberget al2000). This presumably states that the increasing degree
of bias due to high-redshift galaxies being rare objects swamps the gravitational
evolution of density fluctuations.
A number of authors have pointed out that the detailed spectral shape
inferred from galaxy data appears to be inconsistent with that of nonlinear