Beyond ΛCDM: Testing Modified Gravity in the Precision Era of Cosmology

The standard ΛCDM model has been remarkably successful in describing the evolution of our Universe. However, as we enter the precision era of cosmology, the model faces significant challenges, most notably the persistent H0 and S8 tensions. These discrepancies suggest that new physics beyond the standard paradigm may be required to reconcile early-time and late-time observations. In this talk, I will discuss the advantages and cosmological implications of several classes of modified gravity models, including Horndeski gravity, Teleparallel f(T) gravity and modified entropy models. By confronting these models with a diverse array of observational data, I will demonstrate how these theories can modify the expansion history and the growth of structure and potentially resolve these tensions