After extensively testing with realistic SDSS-like mock data, we applied Basilisk to SDSS DR-7  to constrain galaxy-halo connection of both: central and satellite galaxies. While agreeing with previous results from galaxy clustering, weak lensing, group catalogues, and previous iterations of satellite kinematics, our constraints are significantly tighter. We also tightly constrain the true scatter in the galaxy-halo connection.

Basilisk does not assume that satellite galaxies follow the NFW profile of underlying dark matter distribution. Rather it uses a generalised-NFW profile with flexible inner slope and concentration. Using SDSS data, we find that satellite distribution is consistent with a cuspy profile but with a larger scale radius, or lower concentration compared to dark matter. We rule out NFW distribution with  > 5 sigma confidence.

Using full projected phase-space information, Basilisk breaks the mass-anisotropy degeneracy and hence can constrain velocity anisotropy parameter of satellite galaxy orbits. Due to SDSS fiber collision we can not use satellites within 55'' from the central, which excludes most of the inner halo for low mass systems. Thus, the velocity anisotropy of the mass-dependent model is substantially higher in the low mass end, because we only use the satellites in the outer halo for those systems.

With Basilisk, I developed a technique to constrain cosmological parameters, that is free of halo assembly bias and incorporates baryonic effects. It's a novel way to probe the S8 tension, independent of galaxy clustering and weak lensing. Basilisk's inferred cosmology is perfectly consistent with Planck for the fiducial feedback model. The future, with DESI BGS data (20 times larger than SDSS DR-7) looks extremely promising (exact centre of the blue contour is not meaningful).

We use a highly flexible conditional luminosity function (CLF) model (top panel) to statistically link central and satellite galaxies to their respective host haloes. It is flexible enough to capture the curvature of the satellite HOD deviating from a simple power-law (bottom panel), and Basilisk perfectly recovers that deviation introduced in the mock data. Despite these, in a recent paper that I'm about to submit, we show that even such a flexible model can be insufficient to truly capture the galaxy-halo connection in real data. Such lack of flexibility can bias not only galaxy-halo connection inference but also cosmological constraints. This crisis will be even more pronounced with upcoming data from DESI and other surveys. So, we break the traditional CLF model in a very data-driven way and test extensions with the hope of creating more flexible galaxy-halo connection, ready to tackle near-future data.

Cosmological hydrodynamic simulations show that the bound hot gas inside the virial radius is lower than what one would expect from the universal baryon fraction, primarily because of supernova and AGN feedback blowing gas out to larger distances. This decrement is stronger in lower mass haloes because of their shallower potential and inability to hold on to the CGM gas. This effectively translates to lower mass within virial radius in hydro-sims compared to dark matter only (DMO) matched haloes. This affects kinematics of satellite galaxies by lowering their velocity dispersion, and Basilisk's modelling is highly sensitive to that. Our cosmology constraints change based on the strength of feedback we choose. But for the whole range of expected feedback strength, based on EAGLE simulation, our cosmology inference agrees with Planck. With DESI BGS the contour will shrink significantly. Thus demanding in cosmology inference Basilisk will be able to tightly constrain subgrid prescriptions of supernova and AGN feedback in simulations and semi-analytic models (SAMs).