Response approach to the squeezed-limit bispectrum: application to the correlation of quasar and Lyman-$\alpha$ forest power spectrum

Abstract

The squeezed-limit bispectrum, which is generated by nonlinear gravitational evolution as well as inflationary physics, measures the correlation of three wavenumbers, in the configuration where one wavenumber is much smaller than the other two. Since the squeezed-limit bispectrum encodes the impact of a large-scale fluctuation on the small-scale power spectrum, it can be understood as how the small-scale power spectrum "responds" to the large-scale fluctuation. Viewed in this way, the squeezed-limit bispectrum can be calculated using the response approach even in the cases which do not submit to perturbative treatment. To illustrate this point, we apply this approach to the cross-correlation between the large-scale quasar density field and small-scale Lyman-$\alpha$ forest flux power spectrum. In particular, using separate universe simulations which implement changes in the large-scale density, velocity gradient, and primordial power spectrum amplitude, we measure how the Lyman-$\alpha$ forest flux power spectrum responds to the local, long-wavelength quasar overdensity, and equivalently their squeezed-limit bispectrum. We perform a Fisher forecast for the ability of future experiments to constrain local non-Gaussianity using the bispectrum of quasars and the Lyman-$\alpha$ forest. Combining with quasar and Lyman-$\alpha$ forest power spectra to constrain the biases, we find that for DESI the expected $1-\sigma$ constraint is $\mathrm{err}[f_{\mathrm{NL}}]\sim 60$. Ability for DESI to measure $f_{\mathrm{NL}}$ through this channel is limited primarily by the aliasing and instrumental noise of the Lyman-$\alpha$ forest flux power spectrum. The combination of response approach and separate universe simulations provides a novel technique to explore the constraints from the squeezed-limit bispectrum between different observables.

20 pages, 4 figures; matches JCAP accepted version

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Cited by in corpus (16)

• Large-scale dark matter simulations
• Complete super-sample lensing covariance in the response approach
• Scale-dependent bias and bispectrum in neutrino separate universe simulations
• Responses in Large-Scale Structure
• Position-dependent power spectra of the 21-cm signal from the epoch of reionization
• The Hunt for Primordial Interactions in the Large Scale Structures of the Universe
• Separate Universe Simulations with IllustrisTNG: baryonic effects on power spectrum responses and higher-order statistics
• The integrated 3-point correlation function of cosmic shear
• The Covariance of Squeezed Bispectrum Configurations
• Response Approach to the Matter Power Spectrum Covariance
• The Weak Lensing Bispectrum Induced By Gravity
• Bispectrum as Baryon Acoustic Oscillation Interferometer
• Estimating the Integrated Bispectrum from Weak Lensing Maps
• Position-Dependent Correlation Function of Weak Lensing Convergence
• Clustering redshifts with the 21cm-galaxy cross-bispectrum
• On Weak Lensing Response Functions