Lensing of the Microwave Background Fluctuations

The images above illustrate the effect of lensing of relatively low spatial frequency MBR fluctuations by higher frequency projected density fluctuations.

The upper left image shows a gaussian filtered gaussian random field which represents the surface potential of the lensing field.

The upper right panel is a gaussian filtered gaussian random field with a larger coherence scale which represents the unlensed MBR fluctuations.

The lower left panel shows how the MBR fluctuations would actually appear after lensing (with a somewhat unrealistically large amplitude for the lensing deflection it should be admitted....)

The lower right panel shows a hig-pass filtered version of the lensed MBR fluctuations, which emphasises the non-gausssian nature of the lensing induced fluctuations.

What we are seeing here is a coupling between the gradient of the unlensed MBR and the projected density fluctuations; the lens induced fluctuations take the form of a gaussian random field modulated by the amplitude of the angular derivative of the low-frequency MBR fluctuations.

This characteristic non-gaussianity may be useful for discriminating between lening induced and intrisic MBR fluctuations at high frequency.

Grey-scale version:

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e-mail: kaiser@ifa.hawaii.edu