Exploring the Properties and Detection Methods of Dark Matter

We review theoretical candidates for dark matter (DM), summarize observational constraints, and present a theoretical study that modifies the gravitational acceleration profile by introducing a phenomenological coupling parameter — the Shashank Constant — which parametrizes a hypothetical additional dark-sector interaction at galactic scales. Using analytic halo models (NFW and cored isothermal) we derive modified rotation curves and show how the Shashank Constant affects inner-rotation profiles. We provide Python code to reproduce the plots and compute constraints from mock rotation-curve data. We discuss implications for direct/indirect detection and suggest future theoretical and observational tests.