4,342 research outputs found
Cosmic structure sizes in generic dark energy models
The maximum allowable size of a spherical cosmic structure as a function of
its mass is determined by the maximum turn around radius , the
distance from its centre where the attraction on a radial test particle due to
the spherical mass is balanced with the repulsion due to the ambient dark
energy. In this work, we extend the existing results in several directions. (a)
We first show that for , the expression for found
earlier using the cosmological perturbation theory, can be derived using a
static geometry as well. (b) In the generic dark energy model with arbitrary
time dependent state parameter , taking into account the effect of
inhomogeneities upon the dark energy as well, where it is shown that the data
constrain , and (c) in the quintessence and the
generalized Chaplygin gas models, both of which are shown to predict structure
sizes consistent with observations.Comment: v2, 19pp; added references and discussions, improved presentation;
accepted in EPJ
Set-partition tableaux and representations of diagram algebras
The partition algebra is an associative algebra with a basis of set-partition
diagrams and multiplication given by diagram concatenation. It contains as
subalgebras a large class of diagram algebras including the Brauer, planar
partition, rook monoid, rook-Brauer, Temperley-Lieb, Motzkin, planar rook
monoid, and symmetric group algebras. We give a construction of the irreducible
modules of these algebras in two isomorphic ways: first, as the span of
symmetric diagrams on which the algebra acts by conjugation twisted with an
irreducible symmetric group representation and, second, on a basis indexed by
set-partition tableaux such that diagrams in the algebra act combinatorially on
tableaux. The first representation is analogous to the Gelfand model and the
second is a generalization of Young's natural representation of the symmetric
group on standard tableaux. The methods of this paper work uniformly for the
partition algebra and its diagram subalgebras. As an application, we express
the characters of each of these algebras as nonnegative integer combinations of
symmetric group characters whose coefficients count fixed points under
conjugation
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