The super-compressible Cosmic Microwave Background

I just came across this blog post, one of a series on cosmology from the African Institute for Mathematical Sciences, which is in Muizenberg near Cape Town, South Africa. I thought I’d reblog it, partly because it’s on a topic I often discuss in talks and partly because I wanted to draw your attention the site and the other interesting posts on it.

In this article Bruce Bassett explains just how much of the information we get from measurements of the Cosmic Microwave Background can be squeezed into precise estimates of just a few parameters. The only point I would add is that this does assume at the outset that all relevant information is contained within the angular power spectrum; that’s not necessarily the case, but we don’t have any compelling evidence that it’s a wrong assumption for the CMB; see here for a previous discussion of this.

Cosmology at AIMS

One of the most striking features about the Cosmic Microwave Background (CMB) is that it is incredibly compressible from an information content point of view. The Planck satellite produced maps with of order a billion pixels whose information could be compressed almost perfectly into a power spectrum of order one thousand real numbers.

This already is a massive compression. But in addition, most of this information can be compressed further into just six of the parameters of the standard model, yielding a total compression of about one billion to one. This is both remarkable and annoying because we want to be surprised and find things that we can’t explain. And if there are things we can’t explain we want to have clear signals data about them, not just vague hints of their existence.

Anyway, to illustrate just how efficient the compression is, I took the binned WMAP 9 TT power spectrum…

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5 Responses to “The super-compressible Cosmic Microwave Background”

  1. In VLBI, many Gigabits of raw radio data can be compressed into a single delay / rate measurement, and then thousands of those delay / rate measurements can be compressed into a single source image or even just a single source position. The VLBI International Celestial Reference frame is based on many millions of such measurements, representing many petabytes of original data, compressed down into a few thousand numbers, or a ~ 10^-13 compression.

  2. telescoper Says:

    That’s very true, but in the context of data analysis the caveat is that such compression only makes sense if you have a model and you should always check that there isn’t something in the data you’re trying to compress that itself provides evidence that the model is incorrect…

  3. It’s not completely correct to say that the theory only has six parameters though, is it? It has six additional parameters over and above all the parameters of the Standard Model Lagrangian, which I think takes the total to 25.

    • telescoper Says:

      You don’t need the standard model Lagrangian to fit the CMB power spectrum…

      • I don’t know what you mean. You don’t actually fit all those parameters, because their values are known from other experiments. But they are necessary parts of the theory without which none of calculations would be possible.

        For instance, the SM parameters determine the relative abundance of protons and neutrons, the process of nucleosynthesis, and ultimately the helium mass fraction, which in turn affects the damping scale. If you didn’t include those numbers in the calculation, the helium fraction would suddenly become another free parameter that needed to be fit.

        Ditto for all sorts of other things, like the Compton scattering cross-section, the effective number of neutrino species etc.

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