Non-Gaussian CMB Simulations

We are putting together a database of non-Gaussian CMB maps on which you can test your statistics. So far we have focused on cosmological non-Gaussianity generated by toplogical defects. Unlike Gaussian theories, where the perturbation evolution equations can be evolved in Fourier space and the statistics of the initial conditions dictate the statistics of the final result, for defect theories the evolution is much more complicated. We have to solve a highly nonlinear system of partial differential equations, within which different scales are strongly coupled to one another, to get an accurate rendition of the evolution of the defect, matter and radiation fields. Furthermore the two fundamental physical length scales in the system - the defect width and the cosmological horizon - differ by around 50 orders of magnitude at the time the CMB is last-scattered. Defect simulations therefore necessarily involve significant truncations, and large lattices are needed to understand and try to control the effect of these.

Small angle cosmic string maps

This is a set of 50 maps with 1282 pixels of the Kaiser-Stebbins effect. The size of the fields are approximately 2 degrees. These maps are made under the following simplifying assumptions
  • The cosmic string network is evolved in Minkowski space (see Coulson et al ).
  • The Minkowski space Einstein equations are solved to first order (see Borrill et al for the formalism)
  • The last scattering surface is assumed to be perfectly homogeneous

To obtain a normalized map you must multiply by 200Gu (where G is Newtons constant and u is the mass per unit length of the network). Current values for Gu are 1-3x10-6.

There are 5 files containing the data for 10 maps each: 1 2 3 4 5

Small angle texture maps

This is work in progress.

Shown here is a preliminary example of a 5 degree field, 1282 pixel, map of the CMB generated on the NERSC Cray J90. On these smallest scales the CMB anisotropies are expected to be dominated by perturbations generated before last-scattering. The texture field, here evolved using the non-linear sigma model, acts as a source for tightly-coupled radiation (both photon and neutrino) and matter fields.

The color scale indicates standard deviations from the mean. The non-gaussianity reveals itself in the presence of high sigma hot and cold spots, thought to be characteristic of textures. An accurate estimate of the frequency distribution of such peaks would provide a powerful observational test of this model.

Pedro G. Ferreira
Last Updated: 24 July 1997