Non Linear Cosmology Program
"Caustics and Cosmological Structures"
11-15 July 2005  Marseille

Scientific Motivation

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.



Suggested bibliography

  1. Caustics 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.
  2. Probing dark matter caustics with weak lensingR. Gavazzi, R. Mohayaee, B. Fort (2005)
  3. Cusps in CDM halos: The density profile of a billion particle halo. J. Diemand, M. Zemp, B. Moore, J. Stadel and M. Carollo (2005)
  4. Adhesive gravitational clustering. T. Buchert and A. Dominguez (2005) review the issue of multi-streaming in cosmological models and coarse-graining in phase space.
  5. A 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.
  6. Universality in the distribution of caustics in the expanding Universe. T. Yano, H. Koyama, T. Buchert and N. Gouda (2004)
  7. Diurnal and Annual Modulation of Cold Dark Matter SignalsFu-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.
  8. Evidence 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.
  9. Gravitational Lensing by Dark Matter CausticsC. Charmousis, V. Onemli, Z. Qiu and P. Sikivie (2003) derive the gravitational lensing signatures of cold dark matter caustics for a variety of cases.
  10. Solar 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.
  11. Caustic Rings and Cold Dark MatterBen Moore (2000)
  12. Evidence 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 law.
  13. The 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.
  14. The 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 (catastrophes).
  15. Caustic 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.
  16. Morphology in Cosmological Gravitational Clustering and Catastrophe Theory. N. Gouda (1998)
  17. Evolution of the Power Spectrum and Self-Similarity in the Expanding One-dimensional Universe. T. Yano and N. Gouda (1998)
  18. The performance of Lagrangian perturbation schemes at high resolution. T. Buchert, G. Karakatsanis, R. Klaffl and P. Schiller (1997)
  19. Nonlinear Growth of Two-dimensional Cosmological Density Fluctuations and Type of Singularity in Accord with the Catastrophe Theory. N. Gouda (1996)
  20. Lagrangian perturbation approach to the formation of large-scale structure. T. Buchert (1996). A tutorial on Lagrangian perturbation theory.
  21. Phase-space 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 structure.
  22. High spatial resolution in three dimensions - A challenge for large-scale structure formation models. T. Buchert and M. Bartelmann (1991)
  23. Non-Linear Growth of One-Dimensional Cosmological Density Fluctuation and Catastrophe Theory  N. Gouda and T. Nakamura (1989)
  24. Non-Linear Growth of Density Fluctuations in the Spherically Symmetric Expanding Universe and Catastrophe Theory. N. Gouda (1989)
  25. The 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.
  26. A 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.
  27. 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.
  28. 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.
  29. Laboratory 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.
  30. Universal power-law tails for singularity-dominated strong fluctuations. M.V. Berry (1982)
  31. Evolution 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).
  32. The 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.
  33. 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.
  34. Focusing and twinkling : critical exponents from catastrophes in non-Gaussian random short waves. M.V. Berry (1977)
  35. Structural Stability and Morphogenesis. R. Thom (1975) is a book on catastrophe theory edited at W.A.Benjamin Inc. Massachusetts.
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