One-point statistics matter in extended cosmologies
  The late universe contains a wealth of information about fundamental physics
and gravity, wrapped up in non-Gaussian fields. To make use of as much
information as possible it is necessary to go beyond two-point statistics.
Rather than going to higher order N-point correlation functions, we demonstrate
that the probability distribution function (PDF) of spheres in the matter field
(a one-point function) already contains a significant amount of this
non-Gaussian information. The matter PDF dissects different density
environments which are lumped together in two-point statistics, making it
particularly useful for probing modifications of gravity or expansion history.
Our approach in Cataneo et. al. 2021 extends the success of Large Deviation
Theory for predicting the matter PDF in $\Lambda$CDM in these ''extended''
cosmologies. A Fisher forecast demonstrates the information content in the
matter PDF via constraints for a Euclid-like survey volume combining the 3D
matter PDF with the 3D matter power spectrum. Adding the matter PDF halves the
uncertainties on parameters in an evolving dark energy model, relative to the
power spectrum alone. Additionally, the matter PDF contains enough non-linear
information to substantially increase the detection significance of departures
from General Relativity, with improvements up to six times the power spectrum
alone. This analysis demonstrates that the matter PDF is a promising
non-Gaussian statistic for extracting cosmological information, particularly
for beyond $\Lambda$CDM models.
