Alleviating Cosmological Tensions in the Topological Dark Energy Framework

Abstract 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 ΛCDM 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 H0 and the sound horizon scale. As a result, the H0 tension is reduced from the ∼5σ level to ∼2σ, while the S8 discrepancy is simultaneously alleviated to ∼1σ. The reconstructed expansion history and growth observables remain in good agreement with current data, and information-criteria analyses demonstrate statistical competitiveness with ΛCDM. 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.