Investigating the H₀ Tension Across Cosmic Epochs Using Dark Energy Frameworks

The ΛCDM model, combining a cosmological constant with cold dark matter, successfully explains a wide range of cosmological observations. However, recent data reveal growing tensions between ΛCDM predictions and observations, most notably the H₀ tension, a persistent discrepancy between the present-day Hubble constant inferred from early- and late-time probes. Despite numerous proposed explanations, no model has yet reconciled this difference while preserving the successes of ΛCDM.

In this work, we explore whether the H₀ tension originates from a particular epoch in the Universe’s history and determine the redshift range most relevant for resolving it. We examine four dark energy (DE) models: 1) the cosmological constant, 2) DE equation-of-state parametrization, 3) DE pressure-density parametrization, and 4) scale-factor parametrization. Using early-time Planck data and late-time Pantheon+, SHOES, and DESI DR2 data, we constrain model parameters and compare the evolution of H(z). We further reconstruct H(z) in a model-independent way using Gaussian Processes. Our findings show that while ΛCDM exhibits discrepancies across all redshifts, alternative DE models show them mainly at low z, suggesting that the H₀ tension likely arises from late-time physics or systematics. This work also has a potential to clarify whether modifying only the DE sector can help resolve the tension.