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

Abstract

The influence of large-scale density fluctuations on structure formationon small scales is described by the three-point correlation function(bispectrum) in the so-called ``squeezed configurations,'' in which onewavenumber, say k3, is much smaller than the other two, i.e., k3 << k1 ≈ k2. This bispectrum is generated by non-lineargravitational evolution and possibly also by inflationaryphysics. In this paper, we use this fact to show that the bispectrum inthe squeezed configurations can be measured withoutemploying three-point function estimators.Specifically, we use the ``position-dependentpower spectrum,'' i.e., the power spectrum measured in smallersubvolumes of the survey (or simulation box), and correlate it with themean overdensity of the corresponding subvolume. This correlationdirectly measures an integral of the bispectrum dominated bythe squeezed configurations. Measuring this correlation is only slightlymore complex than measuring the power spectrum itself, and sidesteps theconsiderable complexity of the full bispectrum estimation. We usecosmological N-body simulations of collisionless particles withGaussian initial conditions to show that the measured correlationbetween the position-dependent power spectrum and the long-wavelengthoverdensity agrees with the theoretical expectation. The position-dependentpower spectrum thus provides a new, efficient, and promising way to measurethe squeezed-limit bispectrum from large-scale structure observations suchas galaxy redshift surveys.