3,118 research outputs found
Asymptotic silence-breaking singularities
We discuss three complementary aspects of scalar curvature singularities:
asymptotic causal properties, asymptotic Ricci and Weyl curvature, and
asymptotic spatial properties. We divide scalar curvature singularities into
two classes: so-called asymptotically silent singularities and non-generic
singularities that break asymptotic silence. The emphasis in this paper is on
the latter class which have not been previously discussed. We illustrate the
above aspects and concepts by describing the singularities of a number of
representative explicit perfect fluid solutions.Comment: 25 pages, 6 figure
An Ecological Risk Model for Early Childhood Anxiety: The Importance of Early Child Symptoms and Temperament
Childhood anxiety is impairing and associated with later emotional disorders. Studying risk factors for child anxiety may allow earlier identification of at-risk children for prevention efforts. This study applied an ecological risk model to address how early childhood anxiety symptoms, child temperament, maternal anxiety and depression symptoms, violence exposure, and sociodemographic risk factors predict school-aged anxiety symptoms. This longitudinal, prospective study was conducted in a representative birth cohort (n=1109). Structural equation modeling was used to examine hypothesized associations between risk factors measured in toddlerhood/preschool (age=3.0 years) and anxiety symptoms measured in kindergarten (age=6.0 years) and second grade (age= 8.0 years). Early child risk factors (anxiety symptoms and temperament) emerged as the most robust predictor for both parent-and child-reported anxiety outcomes and mediated the effects of maternal and family risk factors. Implications for early intervention and prevention studies are discussed
Asymptotic self-similarity breaking at late times in cosmology
We study the late time evolution of a class of exact anisotropic cosmological
solutions of Einstein's equations, namely spatially homogeneous cosmologies of
Bianchi type VII with a perfect fluid source. We show that, in contrast to
models of Bianchi type VII which are asymptotically self-similar at late
times, Bianchi VII models undergo a complicated type of self-similarity
breaking. This symmetry breaking affects the late time isotropization that
occurs in these models in a significant way: if the equation of state parameter
satisfies the models isotropize as regards the shear
but not as regards the Weyl curvature. Indeed these models exhibit a new
dynamical feature that we refer to as Weyl curvature dominance: the Weyl
curvature dominates the dynamics at late times. By viewing the evolution from a
dynamical systems perspective we show that, despite the special nature of the
class of models under consideration, this behaviour has implications for more
general models.Comment: 29 page
Gravity Waves from a Cosmological Phase Transition: Gauge Artifacts and Daisy Resummations
The finite-temperature effective potential customarily employed to describe
the physics of cosmological phase transitions often relies on specific gauge
choices, and is manifestly not gauge-invariant at finite order in its
perturbative expansion. As a result, quantities relevant for the calculation of
the spectrum of stochastic gravity waves resulting from bubble collisions in
first-order phase transitions are also not gauge-invariant. We assess the
quantitative impact of this gauge-dependence on key quantities entering
predictions for gravity waves from first order cosmological phase transitions.
We resort to a simple abelian Higgs model, and discuss the case of R_xi gauges.
By comparing with results obtained using a gauge-invariant Hamiltonian
formalism, we show that the choice of gauge can have a dramatic effect on
theoretical predictions for the normalization and shape of the expected gravity
wave spectrum. We also analyze the impact of resumming higher-order
contributions as needed to maintain the validity of the perturbative expansion,
and show that doing so can suppress the amplitude of the spectrum by an order
of magnitude or more. We comment on open issues and possible strategies for
carrying out "daisy resummed" gauge invariant computations in non-Abelian
models for which a gauge-invariant Hamiltonian formalism is not presently
available.Comment: 25 pages, 10 figure
Self-similar Bianchi models: I. Class A models
We present a study of Bianchi class A tilted cosmological models admitting a
proper homothetic vector field together with the restrictions, both at the
geometrical and dynamical level, imposed by the existence of the simply
transitive similarity group. The general solution of the symmetry equations and
the form of the homothetic vector field are given in terms of a set of
arbitrary integration constants. We apply the geometrical results for tilted
perfect fluids sources and give the general Bianchi II self-similar solution
and the form of the similarity vector field. In addition we show that
self-similar perfect fluid Bianchi VII models and irrotational Bianchi
VI models do not exist.Comment: 14 pages, Latex; to appear in Classical and Quantum Gravit
A new proof of the Bianchi type IX attractor theorem
We consider the dynamics towards the initial singularity of Bianchi type IX
vacuum and orthogonal perfect fluid models with a linear equation of state. The
`Bianchi type IX attractor theorem' states that the past asymptotic behavior of
generic type IX solutions is governed by Bianchi type I and II vacuum states
(Mixmaster attractor). We give a comparatively short and self-contained new
proof of this theorem. The proof we give is interesting in itself, but more
importantly it illustrates and emphasizes that type IX is special, and to some
extent misleading when one considers the broader context of generic models
without symmetries.Comment: 26 pages, 5 figure
G_2 cosmological models separable in non-comoving coordinates
We study new separable orthogonally transitive abelian G_2 on S_2 models with
two mutually orthogonal integrable Killing vector fields. For this purpose we
consider separability of the metric functions in a coordinate system in which
the velocity vector field of the perfect fluid does not take its canonical
form, providing thereby solutions which are non-separable in comoving
coordinates in general. Some interesting general features concerning this class
of solutions are given. We provide a full classification for these models and
present several families of explicit solutions with their properties.Comment: latex, 26 pages, accepted for publication in Class. Quantum Gra
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