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 L 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 LCDM models.

Automated summary

The probability distribution function (PDF) of matter contains significant non-Gaussian information that can be used to probe modifications of gravity or expansion history. Combining the matter PDF with the power spectrum can substantially reduce parameter uncertainties and increase the detection significance of departures from General Relativity.