Surajit Kalita, Akhil Uniyal, Tomasz Bulik, Yosuke Mizuno

A major issue in contemporary cosmology is the persistent discrepancy, known as the Hubble tension, between the Hubble constant ($H_0$) estimates from local measurements and those inferred from early-Universe observations under the standard $\Lambda$ cold dark matter ($\Lambda$CDM) paradigm. Recent advances have identified fast radio bursts (FRBs), a class of extragalactic phenomena observable at considerable redshifts, as a promising observational tool for probing late-time cosmology. In this study, we incorporate two complementary methodologies, machine learning algorithms and Bayesian analysis, on a set of localized FRBs to rigorously test the consistency of the $\Lambda$CDM model at late cosmic epochs. Our results reveal a statistically significant redshift-dependent variation of $H_0$, which contradicts the core postulate of $\Lambda$CDM. We further validate that the redshift dependency of $H_0$ can be removed within the more flexible framework of $w_0w_a$CDM model. These findings highlight that the redshift evolution of $H_0$ is not merely an artifact of the standard model but an indication of a deeper inadequacy in the $\Lambda$CDM model, supporting the need for a more flexible cosmological framework.