Linear Cosmology Program
and Cosmological Structures"
July 2005 Marseille
The goal of the Non Linear Cosmology Program
(NLCP) is to bring together specialists on nonlinear approaches in cosmology,
physics, astronomy and mathematics, to work on the dynamics of cosmic structures.
The previous workshops were held in Nice, they were devoted to "reconstruction
methods". This year's topic focuses on the formation and the analysis of
Dark Matter Caustics.
Dark Matter is the main gravitational source
in the universe that intervenes in the formation of cosmological structures.
Its identification is still enigmatic and stands for a priority research
program in astroparticles physics. Because of its weakly interacting property,
one can expect that the morphological signature of its distribution in
space stands for a characteristics on its own dynamics. In particular,
caustics are high densities structures that form in collisionless media.
Whereas true singularities result from monokinetics initial conditions,
slightly thicker structures are expected because of residual thermal motions
at decoupling era. If anihilation process take place in these regions,
spectral features of the resulting radiation should provide us with constraints
upon dark matter candidates.
On dynamical grounds, caustics formation
cannot be resolved by numerical approaches, and it is necessary to improve
our knowledge for deriving (semi)analytic approximations that describe
the formation of large scale structures. Caustics are also intimately connected
to multistreams, which is an essential factor on reconstruction problems.
in dark matter halos, R. Mohayaee and S.F. Shandarin
(2005) derive semianalytically the limits on density in the region of caustics
due to thermal velocity dispersion of dark matter particles.
dark matter caustics with weak lensing. R. Gavazzi, R. Mohayaee,
B. Fort (2005)
in CDM halos: The density profile of a billion particle halo. J.
Diemand, M. Zemp, B. Moore, J. Stadel and M. Carollo (2005)
gravitational clustering. T. Buchert and A. Dominguez (2005)
review the issue of multi-streaming in cosmological models and coarse-graining
in phase space.
Cosmological Kinetic Theory for the Evolution of Cold Dark Matter Halos
with Substructure: Quasi-Linear Theory. C.-P. Ma and E. Berschinger
(2004) give applications to galaxy halos.
in the distribution of caustics in the expanding Universe. T. Yano,
H. Koyama, T. Buchert and N. Gouda (2004)
and Annual Modulation of Cold Dark Matter Signals. Fu-Sin
Ling, P. Sikivie and S. Wick (2004) derive the diurnal and annual modulation
signatures of a cold dark matter flow in axion and WIMP direct detection
experiments, taking account not only of the orbital motion of the Earth,
but also the gravity of the Sun, the rotation of the Earth and the gravitational
field of the Earth.
for Ring Caustics in the Milky Way. P.Sikivie (2003) finds evidence
for caustic rings of dark matter in the Milky Way, again with radii obeying
the a_n \propto 1/n law. The evidence is based upon the existence
of sharprises in the rotation curve of our galaxy and on the appearance
of a triangular feature in an IRAS map of the Galactic plane.
Lensing by Dark Matter Caustics. C. Charmousis, V. Onemli,
Z. Qiu and P. Sikivie (2003) derive the gravitational lensing signatures
of cold dark matter caustics for a variety of cases.
Wakes of Dark Matter Flows. P. Sikivie and S. Wick (2002)
analyze the effect of the gravitational field of the Sun on a cold dark
matter flow in our neighborhood. Describes the caustics (called 'spike'
and 'skirt') that occur in this case.
Rings and Cold Dark Matter. Ben Moore (2000)
for universal structure in galactic halos. W.H. Kinney and P.Sikivie
(2000) analyze the rotation curves of 32 external galaxies and finds evidence
for caustic rings of dark matter with radii obeying the a_n \propto 1/n
caustic ring singularity. P. Sikivie (1999) gives a detailed
description of the structure of caustic rings of dark matter in terms of
the elliptic umbilic catastrophe, emphasizes that caustics will be present
in cold dark matter halos for general model-independent reasons.
geometry of phase mixing. S.Tremaine (1999) discusses the expected
dimensionality of phase-space structures and suggests that the most prominent
features in surveys with K>=D (where D is the dimensionally of the phase
structure and K is the number of observables) will be stable singularities
rings of dark matter. P. Sikivie (1998) shows the existence
of inner caustics in dark matter halos, describes them as caustic rings,
gives a law (a_n \propto 1/n) for the caustic ring radii in the case of
self-similar infall, points to observational evidence for caustic rings
of dark matter.
in Cosmological Gravitational Clustering and Catastrophe Theory. N.
of the Power Spectrum and Self-Similarity in the Expanding One-dimensional
Universe. T. Yano and N. Gouda (1998)
performance of Lagrangian perturbation schemes at high resolution.
Buchert, G. Karakatsanis, R. Klaffl and P. Schiller (1997)
Growth of Two-dimensional Cosmological Density Fluctuations and Type of
Singularity in Accord with the Catastrophe Theory. N. Gouda
perturbation approach to the formation of large-scale structure. T.
Buchert (1996). A tutorial on Lagrangian perturbation theory.
structure of cold dark matter halos. P. Sikivie and J.R. Ipser(1992)
give the general arguments why cold dark matter particles are distributed
on a 3-dim hypersurface in 6-dim phase-space.The appearance of discrete
flows of dark matter and caustics are a direct consequence of this phase-space
spatial resolution in three dimensions - A challenge for large-scale structure
formation models. T. Buchert and M. Bartelmann (1991)
Growth of One-Dimensional Cosmological Density Fluctuation and Catastrophe
Theory N. Gouda and T. Nakamura (1989)
Growth of Density Fluctuations in the Spherically Symmetric Expanding Universe
and Catastrophe Theory. N. Gouda (1989)
large-scale structures of the universe : Turbulence, intermittency, structures
in a self-garvitating medium. S.F. Shandarin, Ya. B. Zeldovich
(1989) give the review of the structure formation and discuss all generic
caustics (including metamorphoses) for the potential mapping in one, two
and three dimensions.
class of solutions in Newtonian cosmology and the pancake theory. T.
Buchert (1989) gives high-resolution calculations and illustrations
of caustics and their metamorphoses in Lagrangian perturbation solutions.
J.W. Bruce. J. Lond. Math. Soc., 33,
375. (1986). What changes for the stability of Lagrangian singularities,
if vorticity is present in the flow.
Singularities of Differentiable Maps. V.I.
Arnol'd, S.M. Gusein--Sade and A.N. Varchenko. Vol. I (1982) &
II (1985) summarize the mathematical theory of Lagrangian and Legendrian
singularities. Edited by Birkhäuser, Boston.
observation of caustics, optical simulation of the motion of particles,
and cosmology. Ya. B. Zeldovich, A.V. Mamaev, S.F. Shandarin
(1983) discuss the relation of gravitational instability in two dimensions
and caustics of geometric optics.
power-law tails for singularity-dominated strong fluctuations. M.V.
of singularities of potential flows in collisionless media and transformations
of caustics in three-dimensional space. V.I. Arnol'd (1982)
gives detailed pictures of caustics and their metamorphoses (in Russian).
large scale structure of the universe. I - General properties One- and
two-dimensional models. V.I. Arnold, S.F. Shandarin, Ya. B.
Zeldovich (1982) give a detailed application of the Lagrange-singularity
theory to two--dimensional cosmological continua.
The elements of the large-scale structure of
the universe. V.I. Arnold, Ya. B. Zeldovich, S.F. Shandarin.
Usp. Math. Nauk 36, 214-216 (1981) discuss some subtle mathematical issues
related to caustics of Lagrangian mappings.
and twinkling : critical exponents from catastrophes in non-Gaussian random
short waves. M.V. Berry (1977)
Structural Stability and Morphogenesis. R.
Thom (1975) is a book on catastrophe theory edited at W.A.Benjamin
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