Dark Sector Interactions: Probing the Hubble Parameter and the Sound Horizon

In this study, we explore the impact of the interacting parameter on dark matter in a model resulting from a parametrization of dark energy density. To ensure a model-independent approach, we treat \( r_d \) as a free parameter, avoiding assumptions about the physics of the early Universe or specific recombination models. This approach allows late-time cosmological observations to directly constrain \( r_d \) along with other parameters. Using recent measurements from the Dark Energy Spectroscopic Instrument (DESI) Year 1, cosmic chronometers (CC) and Pantheon\(^{+}\) supernova (SNe Ia) data, we uncover a significant effect of the interacting parameter on dark matter. Our analysis reveals that while non-interacting models attribute 68.2\% of the cosmic energy density to dark energy, interacting models increase this share to 73.4\%. To further probe these differences, we evaluate the evolution of the deceleration parameter for each model, contrasting them against the \(\Lambda\)CDM paradigm and observational data from CC and SNe Ia measurements. Finally, we apply various statistical metrics to rigorously assess the performance of these models.