Edit: This post has been expanded on here https://arxiv.org/abs/1610.08972
I’m not in the habit of publicly writing about papers. But this one has unfortunately been getting some press, so I thought I should weigh in. The work in question is “Marginal evidence for cosmic acceleration from Type Ia supernovae” (Nielsen et al. Scientific Reports 6). The claim of this paper is that the evidence for the accelerated expansion of the universe from SN Ia is weak (< 3 sigma). The central problem with this work is that it assumes a constant SN Ia population distribution with redshift (Equation 4) when selecting priors for x1 (light-curve shape, i.e., the parameter in the Phillips relation) and color. As shown below, these distributions vary in redshift, both because of selection effects (e.g., it is easier to discover bluer, more-luminous SNe at the higher-redshift end of a magnitude-limited survey), and intrinsic population drift (older galaxies host less-luminous SNe, before standardization). Brighter SNe at high redshift implies less distance (as an increasing function of redshift), which implies less acceleration.
Clearly, one must take account of this properly, which means a model that includes both selection effects and intrinsic population drift (*cough* http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:1507.01602). Let’s say I take the simple step of using the basic model of Nielsen et al., but modeling each category of SN discovery (nearby, Sloan Digital Sky Survey, SuperNova Legacy Survey, Hubble Space Telescope) with its own population mean. (This is still a biased analysis, but again I wanted a simple change.) The chi^2 between, e.g., Milne and LambdaCDM increases from 11.61 to 16.84, pushing the Bayesian Information Criterion above 10 in favor of acceleration (please don’t judge me for using these statistical measures, I just wanted something fast for the purposes of this post). There are other problems with the paper, like the “projection” in Figure 2, but incorrectly modeling the SN population as a function of redshift is the original sin.