220 research outputs found
Does Gravitational Clustering Stabilize On Small Scales?
The stable clustering hypothesis is a key analytical anchor on the nonlinear
dynamics of gravitational clustering in cosmology. It states that on
sufficiently small scales the mean pair velocity approaches zero, or
equivalently, that the mean number of neighbours of a particle remains constant
in time at a given physical separation. In this paper we use N-body simulations
of scale free spectra P(k) \propto k^n with -2 \leq n \leq 0 and of the CDM
spectrum to test for stable clustering using the time evolution and shape of
the correlation function \xi(x,t), and the mean pair velocity on small scales.
For all spectra the results are consistent with the stable clustering
predictions on the smallest scales probed, x < 0.07 x_{nl}(t), where x_{nl}(t)
is the correlation length. The measured stable clustering regime corresponds to
a typical range of 200 \lsim \xi \lsim 2000, though spectra with more small
scale power approach the stable clustering asymptote at larger values of \xi.
We test the amplitude of \xi predicted by the analytical model of Sheth \&
Jain (1996), and find agreement to within 20\% in the stable clustering regime
for nearly all spectra. For the CDM spectrum the nonlinear \xi is accurately
approximated by this model with n \simeq -2 on physical scales \lsim 100-300
h^{-1} kpc for \sigma_8 = 0.5-1, and on smaller scales at earlier times. The
growth of \xi for CDM-like models is discussed in the context of a power law
parameterization often used to describe galaxy clustering at high redshifts.
The growth parameter \epsilon is computed as a function of time and length
scale, and found to be larger than 1 in the moderately nonlinear regime -- thus
the growth of \xi is much faster on scales of interest than is commonly
assumed.Comment: 13 pages, 8 figures included; submitted to MNRA
Three-Point Correlations in f(R) Models of Gravity
Modifications of general relativity provide an alternative explanation to
dark energy for the observed acceleration of the universe. We calculate
quasilinear effects in the growth of structure in f(R) models of gravity using
perturbation theory. We find significant deviations in the bispectrum that
depend on cosmic time, length scale and triangle shape. However the deviations
in the reduced bispectrum Q for f(R) models are at the percent level, much
smaller than the deviations in the bispectrum itself. This implies that
three-point correlations can be predicted to a good approximation simply by
using the modified linear growth factor in the standard gravity formalism. Our
results suggest that gravitational clustering in the weakly nonlinear regime is
not fundamentally altered, at least for a class of gravity theories that are
well described in the Newtonian regime by the parameters G_eff and Phi/Psi.
This approximate universality was also seen in the N-body simulation
measurements of the power spectrum by Stabenau and Jain (2006), and in other
recent studies based on simulations. Thus predictions for such modified gravity
models in the regime relevant to large-scale structure observations may be less
daunting than expected on first principles. We discuss the caveats that apply
to such predictions.Comment: 10 pages, 7 figures, Submitted to PR
The non-linear correlation function and the shapes of virialized halos
The correlation function xi(r) of matter in the non-linear regime is assumed
to be determined by the density profiles rho(r) and the mass distribution n(M)
of virialized halos. The Press--Schechter approach is used to compute n(M), and
the stable clustering hypothesis is used to determine the density profiles of
these Press--Schechter halos. Thus, the shape and amplitude of xi(r) on small
scales is related to the initial power spectrum of density fluctuations.
The case of clustering from scale-free initial conditions is treated in
detail. If n is the slope of the initial power spectrum of density
fluctuations, then stable clustering requires that xi(r)\propto r^{-gamma},
where gamma is a known function of n. If halo--halo correlations can be
neglected, then rho(r)\propto r^{-epsilon}, where epsilon = (gamma+3)/2 =
3(4+n)/(5+n). For all values of n of current interest, this slope is steeper
than the value 3(3+n)/(4+n) that was obtained by Hoffman & Shaham in their
treatment of the shapes of the outer regions of collapsed halos. Our main
result is a prediction for the amplitude of the non-linear correlation
function. The predicted amplitude and its dependence on n are in good
quantitative agreement with N-body simulations of self-similar clustering.
If stable clustering is a good approximation only inside the half-mass radii
of Press--Schechter halos, then the density contrast required for the onset of
stable clustering can be estimated. This density contrast is in the range
~300-600 and increases with the initial slope n, in agreement with estimates
from N-body simulations.Comment: 8 pages, uuencoded, gzipped, postscript, submitted to M
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