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

Abstract

The integrated shear 3-point correlation function ζ± is a higher-order statistic of the cosmic shear field that describes the modulation of the 2-point correlation function ξ± by long-wavelength features in the field. Here, we introduce a new theoretical model to calculate ζ± 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 ζ± 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 ζ± 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 ζ± similarly to how they are currently accounted for on ξ±. Using a simple idealized Fisher matrix forecast for a DES-like survey we find that, compared to ξ±, a combined $\xi _{\pm }\ \&\ \zeta _{\pm }$ analysis can lead to improvements of order $20-40\%$ on the constraints of cosmological parameters such as σ8 or the dark energy equation of state parameter w0. 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 encouraging results motivate future works on the integrated shear 3-point correlation function towards applications to real survey data.

A roadmap to cosmological parameter analysis with third-order shear statistics

“…The first of these is the development of a model for the covariance of third-order statistics, which is essential for a tomographic analysis and will be addressed in the following paper of this series (Linke et al, in prep). Additionally, as mentioned above, our model does not yet incorporate systematic and astrophysical effects, like baryonic feedback or intrinsic alignments of source galaxies (Semboloni et al 2013;Halder & Barreira 2022;Pyne et al 2022). We will develop and test strategies for treating these effects in future works of this series.…”

On weak lensing response functions

“…The second equality is valid in the flat-sky approximation. The lowest-order response function for two-point correlation functions was studied recently in [53,[55][56][57][58]. In figure 4 we show Σ n (θ 12 ) which will be discussed in section 6.…”

“…Isotropy and homogeneity dictates ξ(θ 12 ) only depends on the separation θ 12 = |θ 12 |. For surveys with small sky-coverage and masks with non-trivial topology, response functions defined for twopoint correlation function are easier to implement [53][54][55]. We begin by defining the local estimate of the two-point correlation function (2PCF) ξ(θ 12 ) as…”

KiDS-1000 cosmology: Constraints from density split statistics

“…This can be constructed either from simulations (see, e.g., Harnois-Déraps et al 2021;Zürcher et al 2022, for examples of simulation-based inference using the lensing peak count) or from analytical calculations, where for instance Reimberg & Bernardeau (2018) and Barthelemy et al (2021) made use of large deviation theory (LDT) to model the reduced-shear correction to the aperture mass probability distribution function (PDF). Another approach to access higher-order moments is discussed in Halder et al (2021), Halder & Barreira (2022), and Heydenreich et al (2022), where third-order cosmic shear statistics were modelled directly from the bispectrum. Although, the simulation-based approach has advantages regarding the numerical incorporation of critical systematic effects such as the intrinsic alignment (IA) of galaxies (see, e.g.…”