CMB lensing bi-spectrum: assessing analytical predictions against full-sky lensing simulations

Abstract

Cosmic microwave background (CMB) lensing is an integrated effect whose kernel is greater than half the peak value in the range $1<z<5$. Measuring this effect offers a powerful tool to probe the large-scale structure of the Universe at high redshifts. With the increasing precision of ongoing CMB surveys, other statistics than the lensing power spectrum, in particular the lensing bi-spectrum, will be measured at high statistical significance. This will provide ways to improve the constraints on cosmological models and lift degeneracies. Following on an earlier paper, we test analytical predictions of the CMB lensing bi-spectrum against full-sky lensing simulations, and discuss their validity and limitation in detail. The tree-level prediction of perturbation theory agrees with the simulation only up to $\ell \sim 200$, but the one-loop order allows capturing the simulation results up to $\ell \sim 600$. We also show that analytical predictions based on fitting formulas for the matter bi-spectrum agree reasonably well with simulation results, although the precision of the agreement depends on the configurations and scales considered. For instance, the agreement is at the $10\%$-level for the equilateral configuration at multipoles up to $\ell \sim 2000$, but the difference in the squeezed limit raises to more than a factor of two at $\ell \sim 2000$. This discrepancy appears to come from limitations in the fitting formula of the matter bi-spectrum. We also find that the analytical prediction for the post-Born correction to the bi-spectrum is in good agreement with the simulation. We conclude by discussing the bi-spectrum prediction in some theories of modified gravity.

arXiv comment18 pages, 14 figures

References in corpus (42)

• The cosmological simulation code GADGET-2
• HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
• Efficient Computation of CMB anisotropies in closed FRW models
• 4D Gravity on a Brane in 5D Minkowski Space
• Stable clustering, the halo model and nonlinear cosmological power spectra
• Large-Scale Structure of the Universe and Cosmological Perturbation Theory
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• GADGET: A code for collisionless and gasdynamical cosmological simulations
• Revising the Halofit Model for the Nonlinear Matter Power Spectrum
• Weak Gravitational Lensing of the CMB
• Healthy theories beyond Horndeski
• Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability
• Exploring gravitational theories beyond Horndeski
• Weak Lensing of the CMB: A Harmonic Approach
• A measurement of gravitational lensing of the microwave background using South Pole Telescope data
• Hamiltonian analysis of higher derivative scalar-tensor theories
• Measurement of the Cosmic Microwave Background Polarization Lensing Power Spectrum with the POLARBEAR experiment
• Full-sky Gravitational Lensing Simulation for Large-area Galaxy Surveys and Cosmic Microwave Background Experiments
• A Fitting Formula for the Non-Linear Evolution of the Bispectrum
• Non-linear Evolution of Matter Power Spectrum in Modified Theory of Gravity
• The Atacama Cosmology Telescope: Two-Season ACTPol Lensing Power Spectrum
• Impact of post-Born lensing on the CMB
• Weak lensing of the CMB
• BICEP2 / Keck Array VIII: Measurement of gravitational lensing from large-scale B-mode polarization
• An improved fitting formula for the dark matter bispectrum
• The CMB Bispectrum
• A Perturbative Approach to the Redshift Space Power Spectrum: Beyond the Standard Model
• CMB weak-lensing beyond the Born approximation: a numerical approach
• Modeling the nonlinear clustering in modified gravity models I: A fitting formula for matter power spectrum of f(R) gravity
• Lensing Reconstruction in Post-Born Cosmic Microwave Background Weak Lensing
• Probing cosmology with weak lensing selected clusters I: Halo approach and all-sky simulations
• CMB Lensing Beyond the Power Spectrum: Cosmological Constraints from the One-Point PDF and Peak Counts
• Matter bispectrum of large-scale structure: Three-dimensional comparison between theoretical models and numerical simulations
• Cosmological constraints from Subaru weak lensing cluster counts
• On the effect of non-Gaussian lensing deflections on CMB lensing measurements
• The one-loop matter bispectrum as a probe of gravity and dark energy
• CMB Lensing Bispectrum from Nonlinear Growth of the Large Scale Structure
• Constructing perturbation theory kernels for large-scale structure in generalized cosmologies
• Effect of lensing non-Gaussianity on the CMB power spectra
• Matter bispectrum beyond Horndeski
• The CMB lensing bi-spectrum as a probe of modified gravity theories
• Testing gravity on kiloparsec scales with strong gravitational lenses

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• Fitting the nonlinear matter bispectrum by the Halofit approach
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• New constraints on cosmological modified gravity theories from anisotropic three-point correlation functions of BOSS DR12 galaxies
• Modelling the matter bispectrum at small scales in modified gravity
• Post-Born corrections to the one-point statistics of (CMB) lensing convergence obtained via large deviation theory
• Three-point intrinsic alignments of dark matter halos in the IllustrisTNG simulation
• The integrated angular bispectrum of weak lensing
• Weak Lensing Trispectrum and Kurt-Spectra
• The reconstructed CMB lensing bispectrum
• Higher-Order Spectra of Weak Lensing Convergence Maps in Parameterized Theories of Modified Gravity
• Local environmental dependence on weak-lensing shear statistics
• Probing gravity beyond general relativity with bispectrum multipoles of cosmological tracers: I. Theoretical Foundations