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 formation on small 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., $k_3\ll k_1\approx k_2$. This bispectrum is generated by non-linear gravitational evolution and possibly also by inflationary physics. In this paper, we use this fact to show that the bispectrum in the squeezed configurations can be measured without employing three-point function estimators. Specifically, we use the "position-dependent power spectrum," i.e., the power spectrum measured in smaller subvolumes of the survey (or simulation box), and correlate it with the mean overdensity of the corresponding subvolume. This correlation directly measures an integral of the bispectrum dominated by the squeezed configurations. Measuring this correlation is only slightly more complex than measuring the power spectrum itself, and sidesteps the considerable complexity of the full bispectrum estimation. We use cosmological $N$-body simulations of collisionless particles with Gaussian initial conditions to show that the measured correlation between the position-dependent power spectrum and the long-wavelength overdensity agrees with the theoretical expectation. The position-dependent power spectrum thus provides a new, efficient, and promising way to measure the squeezed-limit bispectrum from large-scale structure observations such as galaxy redshift surveys.

23 pages, 6 figures; dependence on cosmological parameters added; JCAP accepted

References in corpus (2)

• Transients from Initial Conditions in Cosmological Simulations
• On the Robustness of the Acoustic Scale in the Low-Redshift Clustering of Matter

Cited by in corpus (26)

• Separate Universe Simulations
• Super-Sample Signal
• Near optimal bispectrum estimators for large-scale structure
• Perturbative approach to covariance matrix of the matter power spectrum
• What does the Marked Power Spectrum Measure? Insights from Perturbation Theory
• The Effective Halo Model: Creating a Physical and Accurate Model of the Matter Power Spectrum and Cluster Counts
• The squeezed matter bispectrum covariance with responses
• Graph Database Solution for Higher Order Spatial Statistics in the Era of Big Data
• ETHOS -- An effective parametrization and classification for structure formation: the non-linear regime at $z\gtrsim 5$
• The Epoch of Reionization 21-cm Bispectrum: The impact of light-cone effects and detectability
• The Integrated Bispectrum and Beyond
• First Detection of Cosmic Microwave Background Lensing and Lyman-α Forest Bispectrum
• Cosmology with Phase Statistics: Parameter Forecasts and Detectability of BAO
• Quintessential Scale Dependence from Separate Universe Simulations
• On Soft Limits of Large-Scale Structure Correlation Functions
• Consistency Relations in Effective Field Theory
• Separate Universes beyond General Relativity
• Euclid: Covariance of weak lensing pseudo-$C_{\ell }$ estimates. Calculation, comparison to simulations, and dependence on survey geometry
• An Inventory of Bispectrum Estimators for Redshift Space Distortions
• Non-local bispectra from super cosmic variance
• Constraining primordial and gravitational mode coupling with the position-dependent bispectrum of the large-scale structure
• Impact of our local environment on cosmological statistics
• The Impact of ionization Morphology and X-ray Heating on the Cosmological 21cm Skew Spectrum
• A Consistency Relation for the CMB B-mode Polarization in the Squeezed Limit
• Indicator Power Spectra: Surgical Excision of Non-linearities and Covariance Matrices for Counts in Cells
• On Weak Lensing Response Functions