Alleviating Cosmological Tensions in the Topological Dark Energy Framework

Recent cosmological observations have revealed persistent tensions in the inferred values of the Hubble–Lemaître constant and the amplitude of matter fluctuations, challenging the standard $\Lambda$CDM paradigm. In this work, we explore the late-time phenomenology of a topological dark energy (TDE) framework using a joint analysis of cosmic chronometers, DESI baryon acoustic oscillations, redshift-space distortions, and the PantheonPlus and Union3 supernova compilations. We show that TDE naturally accommodates departures from standard expansion history and leads to a correlated shift in $H_0$ and the sound horizon scale. As a result, the $H_0$ tension is reduced from the $\sim 5\sigma$ level to $\sim 2\sigma$, while the $S_8$ discrepancy is simultaneously alleviated to $\sim 1\sigma$. The reconstructed expansion history and growth observables remain in good agreement with current data, and information criteria analyses demonstrate statistical competitiveness with $\Lambda$CDM. Importantly, the inferred sound horizon scale remains consistent with Planck constraints, ensuring compatibility with early-Universe physics. Our results highlight TDE as a viable and testable avenue for resolving late-time cosmological tensions.