Model-agnostic cosmological constraints from the baryon acoustic oscillation feature in redshift space

We develop a framework for self-consistently extracting cosmological information from the clustering of tracers in redshift space, $\textit{without}$ relying on model-dependent templates to describe the baryon acoustic oscillation (BAO) feature. Our approach uses the recently proposed Laguerre reconstruction technique for the BAO feature and its linear point $r_{\rm LP}$, and substantially extends it to simultaneously model the multipoles $\ell=0,2,4$ of the anisotropic galaxy 2-point correlation function (2pcf). The approach is `model-agnostic': it assumes that the non-linear growth of structure smears the BAO feature by an approximately Gaussian kernel with a smearing scale $\sigma_{\rm v}$, but does not assume any fiducial cosmology for describing the shape of the feature itself. Using mock observations for two realistic survey configurations assuming $\Lambda$ cold dark matter ($\Lambda$CDM), combined with Bayesian parameter inference, we show that the linear point $r_{\rm LP}$ and smearing scale $\sigma_{\rm v}$ can be accurately recovered by our method in both existing and upcoming surveys. The precision of the recovery of $r_{\rm LP}$ is always better than $1\%$, while $\sigma_{\rm v}$ can be recovered with $\lesssim10\%$ uncertainty provided the linear galaxy bias $b$ is separately constrained, e.g., using weak lensing observations. Our method is also sensitive to the linear growth rate $f$, albeit with larger uncertainties and systematic errors, especially for upcoming surveys such as DESI. We discuss how our model can be modified to improve the recovery of $f$, such that the resulting constraints on $\{f,\sigma_{\rm v},r_{\rm LP}\}$ can potentially be used as a test of cosmological models including and beyond $\Lambda$CDM.