  The linear point (LP) standard ruler was identified as the basis of a purely
geometric method for exploiting the Baryon Acoustic Oscillations (BAO). The LP
exploits the BAO feature imprinted in the galaxy two-point correlation function
to measure cosmological distances independent of any specific cosmological
model. We forecast the expected precision of future and ongoing spectroscopic
galaxy surveys to measure distances leveraging the linear point. We investigate
the cosmological implications of our forecasted results. We focus in particular
on a relevant working example: the detection of the late-time cosmic
acceleration independent of other cosmological probes. Our findings show that,
even within the LCDM standard cosmological paradigm, estimated distances need
to be reliable over a very wide parameter range in order to realize their
maximum utility. This is particularly relevant if we aim to properly
characterize cosmological tensions. The LP is a promising candidate approach to
achieve this reliability. In contrast, widely employed procedures in BAO
analysis estimate distances keeping fixed cosmological parameters to fiducial
values close to cosmic-microwave-background constraints in flat-LCDM. It is
unclear whether they are purely geometric methods. Moreover, they rely on
untested extrapolations to explore the parameter space away from those fiducial
flat-LCDM values. We recommend that all BAO methodologies be validated across
the full range of models and parameters over which their results are quoted,
first by means of linear predictions and then N-body simulations.
