Towards unveiling the large-scale nature of gravity with the wavelet scattering transform

We present the first application of the Wavelet Scattering Transform (WST) in order to constrain the nature of gravity using the three-dimensional (3D) large-scale structure of the universe. Utilizing the Quijote-MG N-body simulations, we can reliably model the 3D matter overdensity field for the f(R) Hu-Sawicki modified gravity (MG) model down to $k_{\rm max}=0.5$ h/Mpc. Combining these simulations with the Quijote $\nu$CDM collection, we then conduct a Fisher forecast of the marginalized constraints obtained on gravity using the WST coefficients and the matter power spectrum at redshift z=0. Our results demonstrate that the WST substantially improves upon the 1$\sigma$ error obtained on the parameter that captures deviations from standard General Relativity (GR), yielding a tenfold improvement compared to the corresponding matter power spectrum result. At the same time, the WST also enhances the precision on the $\Lambda$CDM parameters and the sum of neutrino masses, by factors of 1.2-3.4 compared to the matter power spectrum, respectively. Despite the overall reduction in the WST performance when we focus on larger scales, it still provides a relatively $4.5\times$ tighter 1$\sigma$ error for the MG parameter at $k_{\rm max}=0.2$ h/Mpc, highlighting its great sensitivity to the underlying gravity theory. This first proof-of-concept study reaffirms the constraining properties of the WST technique and paves the way for exciting future applications in order to perform precise large-scale tests of gravity with the new generation of cutting-edge cosmological data.