The cosmic web connection to the dark matter halo distribution through gravity.

In this letter we investigate the connection between the cosmic web and the halo distribution through the gravitational potential. We combine three fields of research, cosmic web classification, perturbation theory expansions of the halo bias, and halo (galaxy) mock catalog making methods. In particular, we use the invariants of the tidal field tensor as generating functions (dubbed I-web), to reproduce the halo number counts of a reference catalog from full gravity calculations, populating the dark matter field on a mesh well into the non-linear regime ($\sim5$ Mpc scales). Our results show an unprecedented agreement with the reference power spectrum within 0.5% up to $k=0.72\,h$ Mpc$^{-1}$. By analysing the three point statistics on large scales (configurations of up to $k=0.2\,h$ Mpc$^{-1}$), we find evidence for non-local bias at the 4.8 $\sigma$ confidence level (an information gain of $\sim$ 3.4 $\sigma$ over the commonly used T-web), being fully compatible with the reference catalog. In particular, we find that a detailed description of tidal anisotropic clustering on large scales is crucial to achieve this accuracy. We conclude that the I-web can potentially be useful to study the cosmic web, to improve the generation of mock galaxy catalogs, to improve on halo mass reconstructions, to study primordial non-Gaussianities, to develop new effective Eulerian galaxy bias models at the field level, and to investigate galaxy evolution improving on environmental studies.