1,018 research outputs found
A comparison of estimators for the two-point correlation function
Nine of the most important estimators known for the two-point correlation
function are compared using a predetermined, rigorous criterion. The indicators
were extracted from over 500 subsamples of the Virgo Hubble Volume simulation
cluster catalog. The ``real'' correlation function was determined from the full
survey in a 3000Mpc/h periodic cube. The estimators were ranked by the
cumulative probability of returning a value within a certain tolerance of the
real correlation function. This criterion takes into account bias and variance,
and it is independent of the possibly non-Gaussian nature of the error
statistics. As a result for astrophysical applications a clear recommendation
has emerged: the Landy & Szalay (1993) estimator, in its original or grid
version Szapudi & Szalay (1998), are preferred in comparison to the other
indicators examined, with a performance almost indistinguishable from the
Hamilton (1993) estimator.Comment: aastex, 10 pages, 1 table, 1 figure, revised version, accepted in
ApJ
Minkowski functionals in cosmology
Minkowski functionals provide a novel tool to characterize the large-scale galaxy distribution in the Universe. Here we give a brief tutorial on the basic features of these morphological measures and indicate their practical application for simulation data and galaxy redshift catalogues as examples
Minkowski Functionals of Abell/ACO Clusters
We determine the Minkowski functionals for a sample of Abell/ACO clusters,
401 with measured and 16 with estimated redshifts. The four Minkowski
functionals (including the void probability function and the mean genus)
deliver a global description of the spatial distribution of clusters on scales
from to 60\hMpc with a clear geometric interpretation. Comparisons with
mock catalogues of N--body simulations using different variants of the CDM
model demonstrate the discriminative power of the description. The standard CDM
model and the model with tilted perturbation spectrum cannot generate the
Minkowski functionals of the cluster data, while a model with a cosmological
constant and a model with breaking of the scale invariance of perturbations
(BSI) yield compatible results.Comment: 10 pages, 13 Postscript figures, uses epsf.sty and mn.sty (included),
submitted to MNRA
Morphological fluctuations of large-scale structure: the PSCz survey
In a follow-up study to a previous analysis of the IRAS 1.2Jy catalogue, we quantify the morphological fluctuations in the PSCz survey. We use a variety of measures, among them the family of scalar Minkowski functionals. We confirm the existence of significant fluctuations that are discernible in volume-limited samples out to 200Mpc/h. In contrast to earlier findings, comparisons with cosmological N-body simulations reveal that the observed fluctuations roughly agree with the cosmic variance found in corresponding mock samples. While two-point measures, e.g. the variance of count-in-cells, fluctuate only mildly, the fluctuations in the morphology on large scales indicate the presence of coherent structures that are at least as large as the sample
Backreaction in Late-Time Cosmology
We review the effect of the formation of nonlinear structures on the expansion rate, spatial curvature, and light propagation in the universe, focusing on the possibility that this effect could explain cosmological observations without requiring the introduction of dark energy or modified gravity. We concentrate on explaining the relevant physics and highlighting open questions.Peer reviewe
Dark Energy from structure: a status report
The effective evolution of an inhomogeneous universe model in any theory of
gravitation may be described in terms of spatially averaged variables. In
Einstein's theory, restricting attention to scalar variables, this evolution
can be modeled by solutions of a set of Friedmann equations for an effective
volume scale factor, with matter and backreaction source terms. The latter can
be represented by an effective scalar field (`morphon field') modeling Dark
Energy.
The present work provides an overview over the Dark Energy debate in
connection with the impact of inhomogeneities, and formulates strategies for a
comprehensive quantitative evaluation of backreaction effects both in
theoretical and observational cosmology. We recall the basic steps of a
description of backreaction effects in relativistic cosmology that lead to
refurnishing the standard cosmological equations, but also lay down a number of
challenges and unresolved issues in connection with their observational
interpretation.
The present status of this subject is intermediate: we have a good
qualitative understanding of backreaction effects pointing to a global
instability of the standard model of cosmology; exact solutions and
perturbative results modeling this instability lie in the right sector to
explain Dark Energy from inhomogeneities. It is fair to say that, even if
backreaction effects turn out to be less important than anticipated by some
researchers, the concordance high-precision cosmology, the architecture of
current N-body simulations, as well as standard perturbative approaches may all
fall short in correctly describing the Late Universe.Comment: Invited Review for a special Gen. Rel. Grav. issue on Dark Energy, 59
pages, 2 figures; matches published versio
On the abundance of collapsed objects
The redshift dependence of the abundance of collapsed objects places strong
constraints on cosmological models of structure formation. We apply a recently
proposed model describing the anisotropic collapse of inhomogeneous spatial
domains. Compared with the spherical top-hat model, this generic model leads to
significantly more collapsed objects at high redshifts: at redshift one and on
the scale of rich clusters a factor of 65. Furthermore, for a fixed
normalization of the initial fluctuation spectrum (\sigma_8=1), we predict four
times as much presently collapsed objects on the mass-scale of rich clusters
within the standard CDM cosmogony, compared to the spherical collapse.Comment: 4 pages, 2 figures, revised version accepted in the ApJ
Can we detect Hot or Cold spots in the CMB with Minkowski Functionals?
In this paper, we investigate the utility of Minkowski Functionals as a probe
of cold/hot disk-like structures in the CMB. In order to construct an accurate
estimator, we resolve a long-standing issue with the use of Minkowski
Functionals as probes of the CMB sky -- namely that of systematic differences
("residuals") when numerical and analytical MF are compared. We show that such
residuals are in fact by-products of binning, and not caused by pixelation or
masking as originally thought. We then derive a map-independent estimator that
encodes the effects of binning, applicable to beyond our present work. Using
this residual-free estimator, we show that small disk-like effects (as claimed
by Vielva et al.) can be detected only when a large sample of such maps are
averaged over. In other words, our estimator is noise-dominated for small disk
sizes at WMAP resolution. To confirm our suspicion, we apply our estimator to
the WMAP7 data to obtain a null result.Comment: 15 pages, 13 figure
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