Systematically calibrate halo-velocity statistics for cosmological constraints

Develop a systematic calibration of the dark-matter-halo peculiar-velocity distribution and its fitted Tsallis parameters, particularly the velocity dispersion and non-extensive index, for constraining cosmological parameters.

Background

The paper demonstrates that the Tsallis distribution describes halo peculiar-velocity distributions across simulations with different cosmological parameters. The fitted velocity dispersion varies substantially between cosmologies, whereas the non-extensive index has comparatively weak discriminating power. These findings suggest that the fitted parameters could be useful for cosmological inference, but the paper does not perform the systematic calibration needed to quantify that application.

The unresolved work concerns determining how the halo velocity-distribution parameters map onto cosmological parameters, including the robustness, sensitivity, and calibration of that relationship across cosmological models and simulation outputs.