Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The probability distribution of cluster formation times and implied
  Einstein Radii   We provide a quantitative assessment of the probability distribution function
of the concentration parameter of galaxy clusters. We do so by using the
probability distribution function of halo formation times, calculated by means
of the excursion set formalism, and a formation redshift-concentration scaling
derived from results of N-body simulations. Our results suggest that the
observed high concentrations of several clusters are quite unlikely in the
standard Lambda CDM cosmological model, but that due to various inherent
uncertainties, the statistical range of the predicted distribution may be
significantly wider than commonly acknowledged. In addition, the probability
distribution function of the Einstein radius of A1689 is evaluated, confirming
that the observed value of ~45" +/- 5" is very improbable in the currently
favoured cosmological model. If, however, a variance of ~20% in the
theoretically predicted value of the virial radius is assumed, than the
discrepancy is much weaker. The measurement of similarly large Einstein radii
in several other clusters would pose a difficulty to the standard model. If so,
earlier formation of the large scale structure would be required, in accord
with predictions of some quintessence models. We have indeed verified that in a
viable early dark energy model large Einstein radii are predicted in as many as
a few tens of high-mass clusters.

23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
2
The categories of this paper are: math
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph