[Paper Review] A Model for the Squeezed Bispectrum in the Non-Linear Regime

Matteo Biagetti, Juan Calles+3 more|arXiv (Cornell University)|Dec 22, 2022

Blind Source Separation Techniques4 citations

TL;DR

This paper develops a response function-based model for the squeezed dark matter bispectrum in the non-linear regime, leveraging consistency relations to constrain the functional form of response coefficients. The model achieves agreement within one standard deviation of simulated data across $k \sim 0.1\text{--}0.7\,h/\text{Mpc}$ at $z=0$, validating its reliability beyond perturbation theory limits.

ABSTRACT

We present a model for the squeezed dark matter bispectrum, where the short modes are deep in the non-linear regime. We exploit the consistency relations for large-scale structures combined with a response function approach to write the squeezed bispectrum in terms of a few unknown functions of the short modes. We provide an ansatz for a fitting function for these response functions, checking that the resulting model is reliable when compared to the one-loop squeezed bispectrum. We then test the model against measured bispectra from numerical simulations for short modes ranging between $k \sim 0.1 \, h/$Mpc, and $k \sim 0.7 \, h/$Mpc at redshift $z=0$. To evaluate the goodness of the fit of our model we implement a non-Gaussian covariance and find agreement within $1$-$σ$ standard deviation of the simulated data.

Motivation & Objective

• To model the squeezed dark matter bispectrum in the non-linear regime where standard perturbation theory fails.
• To leverage consistency relations and response functions to constrain the functional form of the bispectrum in squeezed configurations.
• To test the model against high-precision N-body simulations across a range of non-linear scales.
• To validate the model using a non-Gaussian covariance and assess goodness of fit within statistical uncertainties.

Proposed method

• The authors use a response function approach to model the small-scale density field's response to a long-wavelength perturbation.
• They express the squeezed bispectrum as a sum of response coefficients multiplied by long-wavelength power spectra.
• A fitting function is proposed for the response coefficients, informed by one-loop perturbation theory and numerical simulations.
• The model is calibrated using separate-universe N-body simulations to measure response functions at non-linear scales.
• Theoretical errors are estimated by comparing the response model to the full one-loop perturbation theory bispectrum.
• A non-Gaussian covariance is implemented to rigorously test model agreement with simulated data.

Experimental results

Research questions

• RQ1 Can the response function approach accurately model the squeezed bispectrum in the deeply non-linear regime?
• RQ2 How well does the model reproduce simulated bispectra across $k \sim 0.1\text{--}0.7\,h/\text{Mpc}$ at $z=0$?
• RQ3 Does the model remain consistent with the consistency relation in the squeezed limit despite non-linear dynamics?
• RQ4 What is the impact of non-Gaussian covariance on the model's goodness of fit?
• RQ5 Can the response coefficients be reliably fitted with a simple parametric form in the non-linear regime?

Key findings

• The model achieves agreement with simulated bispectra within one standard deviation when using a non-Gaussian covariance.
• The response function fitting function successfully captures the non-linear behavior of the bispectrum across the tested $k$-range.
• Theoretical errors estimated from the one-loop SPT bispectrum are robust, with Z-values of the order of one standard deviation.
• The model remains consistent with the late-time consistency relation, showing no divergent $q^{-2}$ or $q^{-1}$ poles in the squeezed limit.
• The response coefficients derived from loop integrals depend only on terms independent of $\mu$ or quadratic in $\mu$, validating the response function hypothesis at one-loop order.
• The model provides a reliable, non-perturbative description of the squeezed bispectrum beyond the reach of standard perturbation theory.