Position-dependent power spectrum of the large-scale structure: a novel method to measure the squeezed-limit bispectrum

摘要

The influence of large-scale density fluctuations on structure formation onsmall scales is described by the three-point correlation function (bispectrum)in the so-called "squeezed configurations," in which one wavenumber, say $k_3$,is much smaller than the other two, i.e., $k_3\ll k_1\approx k_2$. Thisbispectrum is generated by non-linear gravitational evolution and possibly alsoby inflationary physics. In this paper, we use this fact to show that thebispectrum in the squeezed configurations can be measured without employingthree-point function estimators. Specifically, we use the "position-dependentpower spectrum," i.e., the power spectrum measured in smaller subvolumes of thesurvey (or simulation box), and correlate it with the mean overdensity of thecorresponding subvolume. This correlation directly measures an integral of thebispectrum dominated by the squeezed configurations. Measuring this correlationis only slightly more complex than measuring the power spectrum itself, andsidesteps the considerable complexity of the full bispectrum estimation. We usecosmological $N$-body simulations of collisionless particles with Gaussianinitial conditions to show that the measured correlation between theposition-dependent power spectrum and the long-wavelength overdensity agreeswith the theoretical expectation. The position-dependent power spectrum thusprovides a new, efficient, and promising way to measure the squeezed-limitbispectrum from large-scale structure observations such as galaxy redshiftsurveys.