skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Response approach to the squeezed-limit bispectrum: application to the correlation of quasar and Lyman-α forest power spectrum

Abstract

We present 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-α 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-α 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-α forest. Combining with quasar and Lyman-α forest power spectra to constrain the biases, we find that for DESI the expectedmore » 1-σ constraint is err[f NL]~60. Ability for DESI to measure f NL through this channel is limited primarily by the aliasing and instrumental noise of the Lyman-α forest flux power spectrum. Lastly, 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.« less

Authors:
 [1];  [2];  [3];  [2]
  1. Stony Brook Univ., NY (United States). C.N. Yang Institute for Theoretical Physics
  2. Brookhaven National Lab. (BNL), Upton, NY (United States)
  3. Max Planck Society, Garching (Germany). Max Planck Inst. for Astrophysics
Publication Date:
Research Org.:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1376138
Report Number(s):
BNL-114076-2017-JA
Journal ID: ISSN 1475-7516
Grant/Contract Number:
SC0012704
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Cosmology and Astroparticle Physics
Additional Journal Information:
Journal Volume: 2017; Journal Issue: 06; Journal ID: ISSN 1475-7516
Publisher:
Institute of Physics (IOP)
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; Lyman alpha forest; cosmological parameters from LSS; cosmological simulations

Citation Formats

Chiang, Chi-Ting, Cieplak, Agnieszka M., Schmidt, Fabian, and Slosar, Anže. Response approach to the squeezed-limit bispectrum: application to the correlation of quasar and Lyman-α forest power spectrum. United States: N. p., 2017. Web. doi:10.1088/1475-7516/2017/06/022.
Chiang, Chi-Ting, Cieplak, Agnieszka M., Schmidt, Fabian, & Slosar, Anže. Response approach to the squeezed-limit bispectrum: application to the correlation of quasar and Lyman-α forest power spectrum. United States. doi:10.1088/1475-7516/2017/06/022.
Chiang, Chi-Ting, Cieplak, Agnieszka M., Schmidt, Fabian, and Slosar, Anže. Mon . "Response approach to the squeezed-limit bispectrum: application to the correlation of quasar and Lyman-α forest power spectrum". United States. doi:10.1088/1475-7516/2017/06/022.
@article{osti_1376138,
title = {Response approach to the squeezed-limit bispectrum: application to the correlation of quasar and Lyman-α forest power spectrum},
author = {Chiang, Chi-Ting and Cieplak, Agnieszka M. and Schmidt, Fabian and Slosar, Anže},
abstractNote = {We present 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-α 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-α 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-α forest. Combining with quasar and Lyman-α forest power spectra to constrain the biases, we find that for DESI the expected 1-σ constraint is err[fNL]~60. Ability for DESI to measure fNL through this channel is limited primarily by the aliasing and instrumental noise of the Lyman-α forest flux power spectrum. Lastly, 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.},
doi = {10.1088/1475-7516/2017/06/022},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 06,
volume = 2017,
place = {United States},
year = {Mon Jun 12 00:00:00 EDT 2017},
month = {Mon Jun 12 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on June 12, 2018
Publisher's Version of Record

Citation Metrics:
Cited by: 2works
Citation information provided by
Web of Science

Save / Share:
  • 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 themore » cross-correlation between the large-scale quasar density field and small-scale Lyman-α 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-α 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-α forest. Combining with quasar and Lyman-α forest power spectra to constrain the biases, we find that for DESI the expected 1−σ constraint is err[ f {sub NL}]∼60. Ability for DESI to measure f {sub NL} through this channel is limited primarily by the aliasing and instrumental noise of the Lyman-α 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.« less
  • Current experiments are providing measurements of the flux power spectrum from the Lyman-α forests observed in quasar spectra with unprecedented accuracy. Their interpretation in terms of cosmological constraints requires specific simulations of at least equivalent precision. In this paper, we present a suite of cosmological N-body simulations with cold dark matter and baryons, specifically aiming at modeling the low-density regions of the inter-galactic medium as probed by the Lyman-α forests at high redshift. The simulations were run using the GADGET-3 code and were designed to match the requirements imposed by the quality of the current SDSS-III/BOSS or forthcoming SDSS-IV/eBOSS data.more » They are made using either 2 × 768{sup 3} ≅ 1 billion or 2 × 192{sup 3} ≅ 14 million particles, spanning volumes ranging from (25 Mpc h{sup −1}){sup 3} for high-resolution simulations to (100 Mpc h{sup −1}){sup 3} for large-volume ones. Using a splicing technique, the resolution is further enhanced to reach the equivalent of simulations with 2 × 3072{sup 3} ≅ 58 billion particles in a (100 Mpc h{sup −1}){sup 3} box size, i.e. a mean mass per gas particle of 1.2 × 10{sup 5}M{sub ⊙} h{sup −1}. We show that the resulting power spectrum is accurate at the 2% level over the full range from a few Mpc to several tens of Mpc. We explore the effect on the one-dimensional transmitted-flux power spectrum of four cosmological parameters (n{sub s}, σ{sub 8}, Ω{sub m} and H{sub 0}) and two astrophysical parameters (T{sub 0} and γ) that are related to the heating rate of the intergalactic medium. By varying the input parameters around a central model chosen to be in agreement with the latest Planck results, we built a grid of simulations that allows the study of the impact on the flux power spectrum of these six relevant parameters. We improve upon previous studies by not only measuring the effect of each parameter individually, but also probing the impact of the simultaneous variation of each pair of parameters. We thus provide a full second-order expansion, including cross-terms, around our central model. We check the validity of the second-order expansion with independent simulations obtained either with different cosmological parameters or different seeds. Finally, a comparison to the one-dimensional Lyman-α forest power spectrum obtained with BOSS by [1] shows an excellent agreement.« less
  • We measure the large-scale cross-correlation of quasars with the Lyα forest absorption in redshift space, using ∼ 60000 quasar spectra from Data Release 9 (DR9) of the Baryon Oscillation Spectroscopic Survey (BOSS). The cross-correlation is detected over a wide range of scales, up to comoving separations r of 80 h{sup −1}Mpc. For r > 15 h{sup −1}Mpc, we show that the cross-correlation is well fitted by the linear theory prediction for the mean overdensity around a quasar host halo in the standard ΛCDM model, with the redshift distortions indicative of gravitational evolution detected at high confidence. Using previous determinations ofmore » the Lyα forest bias factor obtained from the Lyα autocorrelation, we infer the quasar bias factor to be b{sub q} = 3.64{sup +0.13}{sub −0.15} at a mean redshift z = 2.38, in agreement with previous measurements from the quasar auto-correlation. We also obtain a new estimate of the Lyα forest redshift distortion factor, β{sub F} = 1.1±0.15, slightly larger than but consistent with the previous measurement from the Lyα forest autocorrelation. The simple linear model we use fails at separations r < 15h{sup −1}Mpc, and we show that this may reasonably be due to the enhanced ionization due to radiation from the quasars. We also provide the expected correction that the mass overdensity around the quasar implies for measurements of the ionizing radiation background from the line-of-sight proximity effect.« less
  • We measure the large-scale cross-correlation of quasars with the Lyα forest absorption, using over 164,000 quasars from Data Release 11 of the SDSS-III Baryon Oscillation Spectroscopic Survey. We extend the previous study of roughly 60,000 quasars from Data Release 9 to larger separations, allowing a measurement of the Baryonic Acoustic Oscillation (BAO) scale along the line of sight c/(H(z = 2.36)r{sub s}) = 9.0±0.3 and across the line of sight D{sub A}(z = 2.36)/r{sub s} = 10.8±0.4, consistent with CMB and other BAO data. Using the best fit value of the sound horizon from Planck data (r{sub s} = 147.49 Mpc),more » we can translate these results to a measurement of the Hubble parameter of H(z = 2.36) = 226±8 km s{sup −1} Mpc{sup −1} and of the angular diameter distance of D{sub A}(z = 2.36) = 1590±60 Mpc. The measured cross-correlation function and an update of the code to fit the BAO scale (baofit) are made publicly available.« less
  • 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{sub 3}, is much smaller than the other two, i.e., k{sub 3} << k{sub 1} ≈ k{sub 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 smallermore » 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.« less