The Hubble Tension: A Review of Early- and Late-Universe Determinations of the Cosmic Expansion Rate and Proposed Theoretical Resolutions

Abstract

The Hubble constant, H0, quantifies the present-day expansion rate of the universe and anchors the cosmic distance scale, the inferred age of the universe, and the dark-energy equation of state. Two independent families of measurement now disagree at a formal significance exceeding 5σ: early-universe inferences from the cosmic microwave background (CMB) and baryon acoustic oscillations (BAO), analyzed within the standard ΛCDM model, yield H0 ≈ 67-68 km s⁻¹ Mpc⁻¹, whereas a broad ensemble of late-universe, largely distance-ladder-based measurements cluster around H0 ≈ 70-75 km s⁻¹ Mpc⁻¹. This review traces the history of H0 measurement, summarizes the theoretical framework relating H0 to the sound horizon and the expansion history, and synthesizes more than a dozen independent early- and late-universe determinations, including distance-ladder, geometric, gravitational-lensing, gravitational-wave, cosmic-chronometer, and quasar-based methods. It tabulates their central values and uncertainties, traces the systematic-error investigations - including recent James Webb Space Telescope Cepheid photometry and revised strong-lensing mass-profile modeling - that have narrowed but not eliminated plausible mundane explanations, and quantifies the statistical robustness of the tension across the full measurement ensemble. It then evaluates the principal theoretical proposals for reconciling the two regimes, spanning early dark energy, evolving dark-energy equations of state motivated by recent DESI results, modified gravity, interacting dark-sector models, and ladder-wide systematics, assessing each against current observational constraints in a summary comparison table. We conclude that the tension is unlikely to be resolved by any single known systematic and outline the observational programs - the Vera C. Rubin Observatory, Euclid, the Nancy Grace Roman Space Telescope, and next-generation gravitational-wave detectors - most likely to discriminate among the competing explanations over the coming decade.