Probing dark matter through gravitational time delay

Astrophysical and cosmological observations indicate that dark matter consists of cold, nonrelativistic particles. When cold dark matter is present, the gravitational field of the galactic halo deviates from the Schwarzschild metric. In this study, we calculated the gravitational time delay experienced by photons, gravitational waves, and neutral particles with mass in the presence of cold dark matter. Additionally, we extend our analysis to alternative models of dark matter such as Weyl gravity and emergent gravity. Our results suggest that differences in the arrival times of photons, gravitational waves and energetic neutrinos from phenomena like supernova explosions or Gamma-Ray Bursts (GRBs) could potentially distinguish between various dark matter models, provided the neutrino mass is independently known.