Skip to content
Skip to navigation menu


CMB maps from anisotropic cosmological models

Simulated maps of the the CMB temperature using Bianchi type cosmologies:  V (left), VII0 (middle) and VIIh (right). The colour scale is marked in milliKelvin.

Here we provide some information about CMB maps developed using anisotropic cosmological models called Bianchi models. Bianchi cosmological models are exact solution to Einstein's Field Equations, like the Friedmann-Roberston-Walker (FRW) solution. However the FRW solution is homogeneous and isotropic, whereas the Bianchi solutions are homogeneous but not isotropic. The Bianchi classification covers the whole set of anistropic cosmological models, and an interesting point to note is that not all of these classes tend to a FRW universe at their limit.

Paper 1: (astro-ph / ads)

This article gives a brief introduction to Bianchi cosmological models and the resulting temperature and polarization maps they produce. It shows that localized features in the temperature maps, perhaps similar to the cold spot observed in the Wilkinson Microwave Anisotropy Probe (WMAP) data, can be generated in models with negative spatial curvature, i.e. Bianchi types V and VIIh. Both these models also generate coherent polarization patterns. In Bianchi VIIh, however, rotation of the polarization angle as light propagates along geodesics can convert E modes into B modes but in Bianchi V this is not necessarily the case. It is therefore possible, at least in principle, to generate localized temperature features without violating existing observational constraints on the odd-parity component of the cosmic microwave background polarization.

Paper 2: (astro-ph / ads)

This article provides more detailed information about Bianchi cosmological models and goes into depth about how the temperature and polarization maps were produced.

Paper 3: (astro-ph / ads)

This article provides provides statistical characterization of the features observed in the CMB maps detailed in Papers 1 and 2. Strong correlations in the maps are identified and metrics proposed to identify these quantities but that are also generic for all form of anisotropy.

Additional Material:

One of the metrics used in this article to quantify correlations in the Bianchi CMB maps are spherical harmonics coefficients. The article references movies of plots of the phase correlations:

Phase differences from Bianchi V CMB Map mpg [3.2 MB].

Phase differences from Bianchi VII0 CMB Map mpg [3.8 MB].

Phase differences from Bianchi VII_h CMB Map mpg [5.4 MB].

See Also