A Fast and Accurate Implementation of the Effective Fluid Approximation for Ultralight Axions

We present a numerically efficient and accurate implementation of the Passaglia-Hu effective fluid approximation for ultralight axions (ULAs) within the Boltzmann code CAMB. This method is specifically designed to evolve the axion field accurately across cosmological timescales, mitigating the challenges associated with its rapid oscillations. Our implementation is based on the latest version of CAMB, ensuring compatibility with other cosmological codes., e.g. for calculating cosmological parameter constraints. Compared to exact solutions of the Klein-Gordon equation, our method achieves sub-percent accuracy in the CMB power spectrum across a broad range of axion masses, from $10^{-28}\,\mathrm{eV}$ to $10^{-24}\,\mathrm{eV}$. We perform Markov Chain Monte Carlo (MCMC) analyses incorporating our implementation, and find improved constraints on the axion mass and abundance compared to previous, simpler fluid-based approximations. For example, using \Planck\ PR4 and DESI BAO data, we find $2\sigma$ upper limits on the axion fraction $f_{\rm ax} < 0.0082$ and physical density $\Omega_{\rm ax}h^2 < 0.0010$ for $m=10^{-28}$ eV. The code is publicly available at \url{https://github.com/adammoss/AxiCAMB}.