How sound are our ultra-light axion approximations?

TL;DR

This paper evaluates the accuracy of the effective fluid approximation for ultra-light axions in cosmology, finding it sufficiently precise for current data but potentially biased in future high-precision measurements, especially if standard parameters are fixed.

Contribution

It provides a detailed comparison between the effective fluid approximation and exact solutions for ULAs, quantifying the approximation's biases in CMB observables across different mass ranges.

Findings

Bias on dark matter fraction less than 1σ with current data

Bias up to 4σ in less reliable approximations for primary CMB anisotropies

Expected bias of 4-20σ if cosmological parameters are fixed, exceeding Fisher approximation validity

Abstract

Ultra-light axions (ULAs) are a promising dark-matter candidate. ULAs may have implications for small-scale challenges to the $\Lambda$CDM model, and arise in string scenarios. ULAs are already constrained by cosmic microwave background (CMB) experiments and large-scale structure surveys, and will be probed with much greater sensitivity by future efforts. It is challenging to compute observables in ULA scenarios with sufficient speed and accuracy for cosmological data analysis because the ULA field oscillates rapidly. In past work, an effective fluid approximation has been used to make these computations feasible. Here this approximation is tested against an exact solution of the ULA equations, comparing the induced error of CMB observables with the sensitivity of current and future experiments. In the most constrained mass range for a ULA dark matter component ($10^{-27}~{\rm eV}\leq m_{\rm ax}\leq 10^{-25}~{\rm eV}$), the induced bias on the allowed ULA fraction of dark matter from Planck data is less than $1\sigma$. In the cosmic-variance limit (including temperature and polarization data), the bias is $\lesssim 2\sigma$ for primary CMB anisotropies, with more severe biases (as high as $\sim 4\sigma$) resulting for less reliable versions of the effective fluid approximation. If all of the standard cosmological parameters are fixed by other measurements, the expected bias rises to $4-20\sigma$ (well beyond the validity of the Fisher approximation), though the required level of degeneracy breaking will not be achieved by any planned surveys.