CMB constraints on dark matter-proton scattering: investigating prior-volume effects using profile likelihoods

TL;DR

This paper uses profile-likelihood methods to derive prior-independent constraints on dark matter-proton scattering from CMB data, highlighting the influence of prior-volume effects on Bayesian limits.

Contribution

It introduces a frequentist approach to constrain dark matter interactions, addressing prior-volume biases present in Bayesian analyses.

Findings

Frequentist constraints are prior-independent and more reliable.

Bayesian limits tend to overestimate constraints due to prior-volume effects.

Prior-volume effects significantly impact dark matter scattering parameter constraints.

Abstract

We present profile-likelihood constraints on velocity-independent dark matter-proton scattering, including cases in which only a fraction of dark matter has such non-gravitational interactions. Frequentist profile-likelihood techniques provide prior-independent constraints, circumventing prior-volume effects that we show arise in Bayesian constraints on this model. In the limit where the scattering cross section or the fraction of interacting dark matter approaches zero, the other interacting dark matter model parameters become unconstrained, causing the posterior distribution to favor that region of parameter space. Using Planck 2018 cosmic microwave background anisotropy data, we find a clear impact of prior-volume effects on the posteriors used to place constraints on dark matter scattering. Compared to the frequentist analysis, the Bayesian method consistently overestimates the constraints on the cross section. Given the potentially biased upper limits on models subject to prior-volume effects, such as this one, we recommend supplementing Bayesian constraints with frequentist statistics to better assess the impact of priors.