The fundamental problem with using Bayesian statistics, as the authors of the paper below rightly point out, is that your results are only as good as your Bayesian priors. The whole point of Bayesian statistics relative to frequentist statistics, is to leverage information you have before you look at the data to maximize the amount of information you can glean from new data.
Previous studies using the dark matter particle paradigm strongly disfavor decaying dark matter models with mean lifetimes of less than many times the age of the universe, unless it is very short lived and in a dynamic equilibrium that keeps the total amount of dark matter almost precisely constant.
For example, as I noted in an answer at the Physics Stack Exchange:
Assuming a dark matter particle paradigm, according to a pre-print by Yang (2015) subsequently published in Physical Review D, the lower bound on the mean lifetime of dark matter particles is seconds. This is roughly years. By comparison the age of the universe is roughly
The authors make a different Bayesian prior assumption that prior decaying dark matter parameter estimates and concludes that in their best fit model, around 3% of cold dark matter decays just prior to recombination. In the conventional cosmology timeline, "recombination" (which is "the epoch during which charged electrons and protons first became bound to form electrically neutral hydrogen atoms") occurs about 370,000 years after the Big Bang (at a redshift of z =1100). This implies dark matter with a mean lifetime of about 12.15 billion years, about ten million times shorter than estimates from previous studies. The new Bayesian prior favors metastable, rather than truly stable, dark matter candidates.
Since this is driven by a choice of Bayesian prior, however, it is worth considering why a scientist might be biased towards a prior that leads to more dark matter decays. The most obvious is that searches for decaying dark matter by looking for dark matter decay signatures provides a motivation for an entire subfield of astronomy studies looking for those signatures that would otherwise be ill-motivated since in the standard ΛCDM model dark matter doesn't decay and there are no dark matter decay signatures to be looking for in these astronomy studies.
A large number of studies, all using Bayesian parameter inference from Markov Chain Monte Carlo methods, have constrained the presence of a decaying dark matter component. All such studies find a strong preference for either very long-lived or very short-lived dark matter.
However, in this letter, we demonstrate that this preference is due to parameter volume effects that drive the model towards the standard ΛCDM model, which is known to provide a good fit to most observational data.
Using profile likelihoods, which are free from volume effects, we instead find that the best-fitting parameters are associated with an intermediate regime where around 3% of cold dark matter decays just prior to recombination. With two additional parameters, the model yields an overall preference over the ΛCDM model of Δχ2≈−2.8 with Planck and BAO and Δχ2≈−7.8 with the SH0ES H0 measurement, while only slightly alleviating the H0 tension.
Ultimately, our results reveal that decaying dark matter is more viable than previously assumed, and illustrate the dangers of relying exclusively on Bayesian parameter inference when analysing extensions to the ΛCDM model.
Emil Brinch Holm, et al., "Discovering a new well: Decaying dark matter with profile likelihoods" arXiv:2211.01935 (November 3, 2022).
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