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The linear point (LP) standard ruler was identified as the basis of a purelygeometric method for exploiting the Baryon Acoustic Oscillations (BAO). The LPexploits the BAO feature imprinted in the galaxy two-point correlation functionto measure cosmological distances independent of any specific cosmologicalmodel. We forecast the expected precision of future and ongoing spectroscopicgalaxy surveys to measure distances leveraging the linear point. We investigatethe cosmological implications of our forecasted results. We focus in particularon a relevant working example: the detection of the late-time cosmicacceleration independent of other cosmological probes. Our findings show that,even within the LCDM standard cosmological paradigm, estimated distances needto be reliable over a very wide parameter range in order to realize theirmaximum utility. This is particularly relevant if we aim to properlycharacterize cosmological tensions. The LP is a promising candidate approach toachieve this reliability. In contrast, widely employed procedures in BAOanalysis estimate distances keeping fixed cosmological parameters to fiducialvalues close to cosmic-microwave-background constraints in flat-LCDM. It isunclear whether they are purely geometric methods. Moreover, they rely onuntested extrapolations to explore the parameter space away from those fiducialflat-LCDM values. We recommend that all BAO methodologies be validated acrossthe full range of models and parameters over which their results are quoted,first by means of linear predictions and then N-body simulations.

Linear Point Standard Ruler: cosmological forecasts for future galaxy surveys. Toward consistent BAO analyses far from a fiducial cosmology