There’s been quite a lot of reaction on the interwebs over the last few days much of it very misleading; here’s a sensible account) to a paper by Nielsen, Guffanti and Sarkar which has just been published online in *Scientific Reports*, an offshoot of *Nature*. I think the above link should take you an “open access” version of the paper but if it doesn’t you can find the arXiv version here. I haven’t cross-checked the two versions so the arXiv one may differ slightly.

Anyway, here is the abstract:

The ‘standard’ model of cosmology is founded on the basis that the expansion rate of the universe is accelerating at present — as was inferred originally from the Hubble diagram of Type Ia supernovae. There exists now a much bigger database of supernovae so we can perform rigorous statistical tests to check whether these ‘standardisable candles’ indeed indicate cosmic acceleration. Taking account of the empirical procedure by which corrections are made to their absolute magnitudes to allow for the varying shape of the light curve and extinction by dust, we find, rather surprisingly, that the data are still quite consistent with a constant rate of expansion.

Obviously I haven’t been able to repeat the statistical analysis but I’ve skimmed over what they’ve done and as far as I can tell it looks a fairly sensible piece of work (although it is a frequentist analysis). Here is the telling plot (from the *Nature* version) in terms of the dark energy (y-axis) and matter (x-axis) density parameters:

Models shown in this plane by a line have the correct balance between Ω_{m}, and Ω_{Λ} to cancel out the decelerating effect of the former against the accelerating effect of the latter (a special case is the origin on the plot, which is called the Milne model and represents an entirely empty universe). The contours show “1, 2 and 3*σ”* contours, regarding all other parameters as nuisance parameters. It is true that the line of no acceleration does go inside the 3*σ*contour so in that sense is not entirely inconsistent with the data. On the other hand, the “best fit” (which is at the point Ω_{m}=0.341, Ω_{Λ}=0.569) *does* represent an accelerating universe.

I am not all that surprised by this result, actually. I’ve always felt that taken on its own the evidence for cosmic acceleration from supernovae alone was not compelling. However, when it is combined with other measurements (particularly of the cosmic microwave background and large-scale structure) which are sensitive to other aspects of the cosmological space-time geometry, the agreement is extremely convincing and has established a standard “concordance” cosmology. The CMB, for example, is particularly sensitive to spatial curvature which, measurements tells us, must be close to zero. The Milne model, on the other hand, has a large (negative) spatial curvature entirely excluded by CMB observations. Curvature is regarded as a “nuisance parameter” in the above diagram.

I think this paper is a worthwhile exercise. Subir Sarkar (one of the authors) in particular has devoted a lot of energy to questioning the standard ΛCDM model which far too many others accept unquestioningly. That’s a noble thing to do, and it is an essential part of the scientific method, but this paper only looks at one part of an interlocking picture. The strongest evidence comes from the cosmic microwave background and despite this reanalysis I feel the supernovae measurements still provide a powerful corroboration of the standard cosmology.

Let me add, however, that the supernovae measurements do not directly measure cosmic acceleration. If one tries to account for them with a model based on Einstein’s general relativity and the assumption that the Universe is on large-scales is homogeneous and isotropic and with certain kinds of matter and energy then the observations do imply a universe that accelerates. Any or all of those assumptions may be violated (though some possibilities are quite heavily constrained). In short we could, at least in principle, simply be interpreting these measurements within the wrong framework, and statistics can’t help us with that!