The direct detection of gravitational waves about a decade ago heralded a new era of multi-messenger astronomy. The world also
subsequently witnessed the first simultaneous observation of gravitational and electromagnetic radiations from a single
astronomical event. The ongoing observations from the second-generation ground-based detectors, advanced LIGO-Virgo-KAGRA, have
delivered several key scientific discoveries. In this talk, I will provide a bird's eye view of the detection techniques behind some
of these key discoveries. In the last part, I will highlight the implications of multi-messenger observations from ultra-dense compact
objects, e.g., neutron stars on the unexplored territory of fundamental physics.
We present a composite framework to explore deviations from ΛCDM by independently parameterizing the background expansion and the growth of cosmic structures. Using current observational data, we find strong indications of deviation from ΛCDM in the background expansion, consistent with recent DESI DR2 results, while no significant departure is observed in the growth sector. This is primarily due to limitations in current growth measurements, making it difficult to distinguish between evolving dark energy and modified gravity. We further show how future high-precision surveys like Euclid can break this degeneracy and decisively test such scenarios.