## Fourier-transforming the Universe

Following the little post I did on Tuesday in reaction to a nice paper on the arXiv by Pontzen et al., my attention was drawn today to another paper e related to the comment I made about using Fourier phases as a diagnostic of pattern morphology. The abstract of this one, by Way et al., is as follows:

We compute the complex 3D Fourier transform of the spatial galaxy distribution in a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields results quite similar to those from the Fast Fourier Transform (FFT) of finely binned galaxy positions. In both cases deconvolution of the sampling window function yields estimates of the true 3D transform. The Fourier amplitudes resulting from this simple procedure yield power spectrum estimates consistent with those from other much more complicated approaches. We demonstrate how the corresponding Fourier phase spectrum lays out a simple and complete characterization of non-Gaussianity that is more easily interpretable than the tangled, incomplete multi-point methods conventionally used. Measurements based on the complex Fourier transform indicate departures from exact homogeneity and isotropy at the level of ∼1% or less. Our model-independent analysis avoids statistical interpretations, which have no meaning without detailed assumptions about a hypothetical process generating the initial cosmic density fluctuations.

It’s obviously an excellent piece of work because it cites a lot of my papers!

But seriously I think it’s very exciting that we now have data sets of sufficient size and quality to allow us to go beyond the relatively crude statistical description provided by the power spectrum.

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November 20, 2015 at 3:40 pm

One of the authors was one of the organizers of the conference you attended a while back.

November 20, 2015 at 6:57 pm

… and one can do the same with spin-2 data… applied here to cosmic shear http://arxiv.org/abs/1401.6842

November 21, 2015 at 12:51 pm

Tom,

Thanks for that. If I recall correctly, you didn’t do anything beyond the power-spectrum in that paper?

Peter