© 2015. The American Astronomical Society. All rights reserved. We derive an analytical expression for a novel large-scale structure observable: the line correlation function. The line correlation function, which is constructed from the three-point correlation function of the phase of the density field, is a robust statistical measure allowing the extraction of information in the nonlinear and non-Gaussian regime. We show that, in perturbation theory, the line correlation is sensitive to the coupling kernel F2, which governs the nonlinear gravitational evolution of the density field. We compare our analytical expression with results from numerical simulations and find a 1σ agreement for separations r ≳ 30 h-1 Mpc. Fitting formulae for the power spectrum and the nonlinear coupling kernel at small scales allow us to extend our prediction into the strongly nonlinear regime, where we find a 1σ agreement with the simulations for r ≳ 2 h-1 Mpc. We discuss the advantages of the line correlation relative to standard statistical measures like the bispectrum. Unlike the latter, the line correlation is independent of the bias, in the regime where the bias is local and linear. Furthermore, the variance of the line correlation is independent of the Gaussian variance on the modulus of the density field. This suggests that the line correlation can probe more precisely the nonlinear regime of gravity, with less contamination from the power spectrum variance.
Wolstenhulme, R., Bonvin, C., & Obreschkow, D. (2015). THREE-POINT PHASE CORRELATIONS: A NEW MEASURE OF NONLINEAR LARGE-SCALE STRUCTURE. The Astrophysical Journal, 804(2), Article 132. https://doi.org/10.1088/0004-637X/804/2/132