How sound are our ultra-light axion approximations?

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 ($10^{-27}\mathrm{eV}\le m_{\mathrm{ax}}\le 10^{-25}\mathrm{eV}$), 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.

22 pages, 16 figures, comments are welcome, updated to align all language with version published in Phys. Rev. D. Results unchanged, additional details on numerical methods provided

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