Dear Boud and other very large scale structure enthusiasts.
I've come back to the issue of what amplitude fluctuations in the 2 point correlation function of quasars or galaxies or whatever should we expect given an assumed non-smooth P(k).
The enclosed figure shows xi(r)s for 4 choices of P(k), smoothed with a gaussian of sigma=15 h-1 Mpc.
The black curves are the CMBFAST prediction for
Omega_m = 0.3 Omega_lambda = 0.7 Omega_b = 0.1 h = 0.6 sigma_8 = 0.6
Note that I prefer the CMBFAST predictions of P(k) to the analytical approximations by Bardeen et al. (1989, BBKS) and others, because the approximations cannot reproduce the wiggles in P(k) that generate power in xi(r).
The cosmological parameters above were chosen to fit well the P(k) that Hoyle et al. (2002, MNRAS 329, 336) measured from the 2dF-10k release of quasars. Here P(k)s are defined as (2*pi)^3 times the Peebles definition (as was done by Hoyle et al.).
I assume (Peebles 1993, eq. [21.40])
xi(r) = 4pi/(2pi)^3 int_0^infty k^2 dk P(k) sin(kr)/(kr)
which I compute with Simpson integration as
xi(r) = 4pi/(2pi)^3 ln(10) int_{-5}^5 k^3 P(k) sin(kr)/(kr) d log k
with a step in log k of 0.01.
The red curves use a spline fit to the Hoyle et al. measurements of P(k) within the interval of wavenumbers where they have measurements, and the CMBFAST prediction outside.
The green curves use the CMBFAST P(k) everywhere, except that the point at log k/h = -1.162 is multiplied by 3.
The blue curves multiply the point at log k/h = -1.162 by 10 instead.
The resulting xi(r) curves show very oscillations of much weaker amplitude than found by Roukema, Mamon & Bajtlik (2002, A&A 382, 397), who smoothed their xi(r)'s with the same 15/h Mpc gaussian. Indeed, RMB found oscillations in xi(r) of amplitude 0.05 for Omega_m=0.3,Omega_lambda=0.7, whereas the oscillations predicted here are at best of 0.002 at separations of around 200/h Mpc, hence 25x smaller.
Even if the RMB xi(r)s are affected by their incorporation of selection effects in the z-direction, this should affect the normalization of xi, but presumably not the amplitude of the oscillations.
Moreover, the Hoyle at al. P(k) produces a minimum of xi(r) at r = 245/h Mpc, whereas RMB predict a maximum at that separation.
This makes me worry that the RMB result is caused by noise...
Please convince me that I am wrong! I need to think again about the (2pi)^3 factor...
cheers
Gary