I have been corresponding with Subir Sarkar, one of the authors of the paper I mentioned a few weeks ago arguing that the evidence for cosmic acceleration was much weaker than previously thought. He believes that the criticisms of Rubin and Hayden (linked to in my post) are deeply flawed. Since he and his coauthors haven’t responded publicly to Rubin and Hayden yet, they graciously let me post a summary of their objections.

Dear Matt,

This concerns the discussion on your blog of our recent paper showing that the evidence for cosmic acceleration from supernovae is only 3 sigma. Your obviously annoyed response is in fact to inflated headlines in the media about our work – our paper does just what it does on the can: “Marginal evidence for cosmic acceleration from Type Ia supernovae“. Nevertheless you make a fair assessment of the actual result in our paper and we are grateful for that.

However we feel you are not justified in going on further to state: “

In the twenty years since it was discovered that the universe was accelerating, people have built that discovery into the standard model of cosmology. They’ve used that model to make other predictions, explaining a wide range of other observations. People have built on the discovery, and their success in doing so is its own kind of evidence”. If you were as expert in cosmology as you evidently are concerning amplitudes you would know that much of the reasoning you allude to is circular. There are also other instances (which we are looking into) of using statistical methods thatthe answer to shore up the ‘standard model’ of cosmology. Does it not worry you that the evidence from supernovae – which is widely believed to be compelling – turns out to be less so when examined closely? There is a danger of confirmation bias in that cosmologists making poor measurements with large systematic uncertainties nevertheless keep finding the ‘right answer’. See e.g. Croft & Dailey (http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:1112.3108) who noted “assume… of the 28 measurements of Omega_Lambda in our sample published since 2003, only 2 are more than 1 sigma from the WMAP results. Wider use of blind analyses in cosmology could help to avoid this”. Unfortunately the situation has not improved in subsequent years.You are of course entitled to air your personal views on your blog. But please allow us to point out that you are being unfair to us by uncritically stating in the second part of your sentence: “

EDIT: More arguments against the paper in question,” in which you link to the arXiv eprint by Rubin & Hayden.pointing out that they made some fairly dodgy assumptionsThese authors make a claim similar to Riess & Scolnic (https://blogs.scientificamerican.com/guest-blog/no-astronomers-haven-t-decided-dark-energy-is-nonexistent/) that we “

assume that the mean properties of supernovae from each of the samples used to measure the expansion history are the same, even though they have been shown to be different and past analyses have accounted for these differences”. In fact we are using(called JLA) as Adam Riess and co. have done in their own analysis (Betouleexactly the same datasetet al, http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:1401.4064). They found stronger evidence for acceleration because of using astatistical method (“constrained \chi^2”). The reason why we find weaker evidence is that we use the Maximum Likelihood Estimator – it isflawedbecause of making “notdodgy assumptions”. We show our results in the same \Omega_\Lambda – \Omega_m plane simply for ease of comparison with the previous result – as seen in the attached plot, the contours move to the right … and now enclose the “no acceleration” line within 3 \sigma. Our analysis isnot– as Brian Schmidt tweeted – “at best unorthodox”… even if this too has been uncritically propagated on social media.In fact the result from our (frequentist) statistical procedure has been

by an independent analysis using a ‘Bayesian Hierarchical Model’ (Shariffconfirmedet al, http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:1510.05954). This is a more sophisticated approach because it does not adopt a Gaussian approximation as we did for the distribution of the light curve parameters (x_1 and c), however their contours are more ragged because of numerical computation limitations.Rubin & Hayden do not mention this paper (although bizarrely they ascribe to us the ‘Bayesian Hierarchical Model’). Nevertheless they find more-or-less the same result as us, namely 3.1 sigma evidence for acceleration, using the same dataset as we did (left panel of their Fig.2). They argue however that there are selection effects in this dataset – which have

notalready been corrected for by the JLA collaboration (which incidentally included Adam Riess, Saul Perlmutter and most other supernova experts in the world). To address this Rubin & Hayden introduce a redshift-dependent prior on the x_1 and c distributions. This increases the significance to 4.2 sigma (right panel of their Fig.2). If such a procedure is indeed valid then it does mark progress in the field, but that does not mean that these authors have “demonstrated errors in (our) analysis” as they state in their Abstract. Their result also begs the question why has the significance increased solittlein going from the initial 50 supernovae which yielded 3.9 sigma evidence for acceleration (Riesset al, http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:astro-ph/9805201) to 740 supernovae in JLA? Maybe… at least to anyone interested in cosmology and fundamental physics!this is newsRubin & Hayden also make the usual criticism that we have ignored evidence from other observations e.g. of baryon acoustic oscillations and the cosmic microwave background. We are of course very aware of these observations but as we say in the paper the interpretation of such data is very model-dependent. For example dark energy has no direct influence on the cosmic microwave background. What is deduced from the data is the spatial curvature (adopting the value of the locally measured Hubble expansion rate H_0) and the fractional matter content of the universe (assuming the primordial fluctuation spectrum to be a close-to-scale-invariant power law). Dark energy is then *assumed* to make up the rest (using the sum rule: 1 = \Omega_m + \Omega_\Lambda for a spatially flat universe as suggested by the data). This need not be correct however if there are in fact other terms that should be added to this sum rule (corresponding to corrections to the Friedman equation to account e.g. for averaging over inhomogeneities or for non-ideal gas behaviour of the matter content). It is important to emphasise that there is no

convincing (i.e. >5 sigma)evidence for dark energy, e.g. the late integrated Sachs-Wolfe effect which induces subtle correlations between the CMB and large-scale structure. Rubin & Hayden even claim in their Abstract (v1) that “dynamicalThe combined analysis of modern cosmological experiments … indicate75 sigma evidence forpositive Omega_\Lambda” – which is surely a joke! Nevertheless this is being faithfully repeated on newsgroups, presumably by those somewhat challenged in their grasp of basic statistics.Apologies for the long post but we would like to explain that the technical criticism of our work by Rubin & Hayden and by Riess & Scolnic is rather disingenuous and it is easy to be misled if you are not an expert. You are entitled to rail against the standards of science journalism but please do not taint us by association.

As a last comment, surely we all want to make progress in cosmology but this will be hard if cosmologists are so keen to cling on to their ‘standard model’ instead of subjecting it to critical tests (as particle physicists continually do to their Standard Model). Moreover the fundamental assumptions of the cosmological model (homogeneity, ideal fluids) have not been tested rigorously (unlike the Standard Model which has been tested at the level of quantum corrections). This is all the more important in cosmology because there is simply

for why \Lambda should be of order H_0^2.no physical explanationBest regards,

Jeppe Trøst Nielsen, Alberto Guffanti and Subir Sarkar

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