Information content in mean pairwise velocity and mean relative velocity between pairs in a triplet

Velocity fields provide a complementary avenue to constrain cosmological information, either through the peculiar velocity surveys or the kinetic Sunyaev Zel'dovich effect. One of the commonly used statistics is the mean radial pairwise velocity. Here, we consider the three-point mean relative velocity (i.e. the mean relative velocities between pairs in a triplet). Using halo catalogs from the Quijote suite of N-body simulations, we first showcase how the analytical prediction for the mean relative velocities between pairs in a triplet achieve better than 4-5% accuracy using standard perturbation theory at leading order for triangular configurations with a minimum separation of r >= 50 h(-1) Mpc. Furthermore, we present the mean relative velocity between pairs in a triplet as a novel probe of neutrino mass estimation. We explored the full cosmological information content of the halo mean pairwise velocities and the mean relative velocities between halo pairs in a triplet. We did this through the Fisher-matrix formalism using 22 000 simulations from the Quijote suite and by considering all triangular configurations with a minimum and a maximum separation of 20 h(-1) Mpc and 120 h(-1) Mpc, respectively. We find that the mean relative velocities in a triplet allows a 1 sigma neutrino mass (M-nu) constraint of 0.065 eV, which is roughly 13 times better than the mean pairwise velocity constraint (0.877 eV). This information gain is not limited to neutrino mass, but it extends to other cosmological parameters: Omega(m), Omega(b), h, n(s), and sigma(8), achieving an information gain of 8.9, 11.8, 15.5, 20.9, and 10.9 times, respectively. These results illustrate the possibility of exploiting the mean three-point relative velocities to constrain the cosmological parameters accurately from future cosmic microwave background experiments and peculiar velocity surveys.