Probing cosmology via the clustering of critical points

Exclusion zones in the cross-correlations between critical points (peak-void, peak-wall, filament-wall, filament-void) of the density field define quasi-standard rulers that can be used to constrain dark matter and dark energy cosmological parameters. The average size of the exclusion zone is found to scale linearly with the typical distance between extrema. The latter changes as a function of the matter content of the universe in a predictable manner, but its comoving size remains essentially constant in the linear regime of structure growth on large scales, unless the incorrect cosmology is assumed in the redshift-distance relation. This can be used to constrain the dark energy parameters when considering a survey that scans a range of redshifts. The precision of the parameter estimation is assessed using a set of cosmological simulations, and is found to be a 4$\sigma$ detection of a change in matter content of 5%, or about 3.8$\sigma$ detection of 50% shift in the dark energy parameter using a full sky survey up to redshift 0.5.