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

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