[Paper Review] Response approach to the integrated shear 3-point correlation function: the impact of baryonic effects on small scales

Anik Halder, Alexandre Barreira|arXiv (Cornell University)|Jan 14, 2022

Galaxies: Formation, Evolution, PhenomenaPhysics and Astronomy90 references14 citations

TL;DR

This paper introduces a response-based theoretical model to accurately predict the integrated shear 3-point correlation function (𝜁±) on small angular scales, incorporating baryonic feedback effects via their impact on the nonlinear matter power spectrum. The method achieves 20–40% improvements in cosmological parameter constraints (e.g., 𝜎8, 𝑤0) when combined with the 2-point correlation function, demonstrating strong potential for enhancing constraints on both cosmology and baryonic feedback models.

ABSTRACT

The integrated shear 3-point correlation function $\zeta_{\pm}$ is a higher-order statistic of the cosmic shear field that describes the modulation of the 2-point correlation function $\xi_{\pm}$ by long-wavelength features in the field. Here, we introduce a new theoretical model to calculate $\zeta_{\pm}$ that is accurate on small angular scales, and that allows to take baryonic feedback effects into account. Our model builds on the realization that the small-scale $\zeta_{\pm}$ is dominated by the nonlinear matter bispectrum in the squeezed limit, which can be evaluated accurately using the nonlinear matter power spectrum and its first-order response functions to density and tidal field perturbations. We demonstrate the accuracy of our model by showing that it reproduces the small-scale $\zeta_{\pm}$ measured in simulated cosmic shear maps. The impact of baryonic feedback enters effectively only through the corresponding impact on the nonlinear matter power spectrum, thereby permitting to account for these astrophysical effects on $\zeta_{\pm}$ similarly to how they are currently accounted for on $\xi_{\pm}$. Using a simple idealized Fisher matrix forecast for a DES-like survey we find that, compared to $\xi_{\pm}$, a combined $\xi_{\pm}\ \&\ \zeta_{\pm}$ analysis can lead to improvements of order $20-40\%$ on the constraints of cosmological parameters such as $\sigma_8$ or the dark energy equation of state parameter $w_0$. We find similar levels of improvement on the constraints of the baryonic feedback parameters, which strengthens the prospects for cosmic shear data to obtain tight constraints not only on cosmology but also on astrophysical feedback models. These are encouraging results that motivate future works on the integrated shear 3-point correlation function towards applications to real survey data.

Motivation & Objective

• To develop a theoretically accurate model for the integrated shear 3-point correlation function 𝜁± on small angular scales where nonlinear and baryonic effects dominate.
• To incorporate baryonic feedback effects into 𝜁± predictions by leveraging their impact on the nonlinear matter power spectrum, avoiding direct modeling of the full bispectrum.
• To assess the cosmological and astrophysical constraints achievable by combining 𝜉± and 𝜁± in a joint analysis, particularly in the presence of baryonic uncertainties.
• To validate the model against simulated cosmic shear maps and demonstrate its robustness across scales.

Proposed method

• The model uses the response approach to perturbation theory, which expresses the squeezed-limit matter bispectrum in terms of the nonlinear matter power spectrum and its first-order response functions to density and tidal field perturbations.
• The response functions are calibrated using gravity-only N-body simulations, enabling accurate prediction of the small-scale 𝜁± without requiring full nonlinear bispectrum calculations.
• The method treats baryonic feedback effects indirectly by applying them to the nonlinear matter power spectrum, using the HMCODE formalism as a representative model.
• The theoretical prediction of 𝜁± is validated by comparing it directly with measurements from simulated cosmic shear maps down to 5 arcmin scales.
• A Fisher matrix forecast is employed for a tomographic DES-like survey to quantify improvements in cosmological and feedback parameter constraints.
• The analysis includes marginalization over baryonic feedback parameters (𝜂0, 𝑐min) to assess robustness to uncertainties in astrophysical modeling.

Experimental results

Research questions

• RQ1 Can the response approach accurately model the small-scale integrated shear 3-point correlation function 𝜁± in the nonlinear regime?
• RQ2 How do baryonic feedback effects influence 𝜁±, and can they be effectively incorporated via their impact on the nonlinear matter power spectrum?
• RQ3 To what extent does combining 𝜉± and 𝜁± improve constraints on cosmological parameters like 𝜎8 and 𝑤0 compared to using 𝜉± alone?
• RQ4 What is the gain in constraining power for baryonic feedback parameters when including 𝜁± in the analysis, even after marginalizing over uncertainties?
• RQ5 Which angular scales remain robust to baryonic effects when using 𝜁± in data analysis?

Key findings

• The response-based model accurately reproduces 𝜁± measured in simulated cosmic shear maps down to 5 arcmin angular scales, validating its predictive power in the highly nonlinear regime.
• The inclusion of 𝜁± in a joint analysis with 𝜉± improves constraints on cosmological parameters such as 𝜎8 and 𝑤0 by 20–40% in a DES-like Fisher forecast.
• Even after marginalizing over baryonic feedback uncertainties, the addition of small-scale 𝜁± data leads to 15–20% tighter constraints on 𝑤0 compared to scale-cuts that exclude nonlinear scales.
• The method enables significant improvements—up to 20–30%—in constraints on the baryonic feedback parameters 𝜂0 and 𝑐min, demonstrating its utility for probing astrophysical feedback models.
• The impact of baryonic feedback on 𝜁± is effectively captured through its influence on the nonlinear matter power spectrum, allowing seamless integration with existing modeling frameworks.