Competing Models of Cosmic Acceleration: A Comparative Review Using a Late-Time, Model-Independent Hubble Constant

In this review, we compare the H 0 values derived from four representative cosmic acceleration models—ΛCDM, w 0 w a CDM, βϕCDM, and Hu–Sawicki ƒ(R) gravity—against a unified late-time, dark-energy-model-independent calibration of H 0 . This work does not conduct a new likelihood analysis, but rather collects results from completed studies and synthesizes data to provide a systematic comparison of the considered cosmological models. The reference H 0 is derived using the inverse distance ladder method, which yields a value of H 0 =66.82±0.74 kms -1 Mpc -1 . This establishes a common benchmark against which the estimations of the different cosmological models can be evaluated. For each model, a two-metric evaluation is conducted: the deviation of its inferred from this reference is expressed by the Gaussian tension, and the Bayesian evidence is considered simultaneously to account for the trade-off between goodness of fit and model complexity. In terms of the tension, none of the four models exhibits a statistically significant departure from the reference value, with all inferred H 0 values remaining within approximately 1.3σ. Similarly, the Bayesian evidence also indicates no strong preference toward any beyond-ΛCDM models. When combined for an integrated analysis, these results do not provide compelling evidence that any of the evaluated late-time extensions offers a decisive improvement over the standard ΛCDM model; thus, this baseline framework remains as the most parsimonious and well-supported reference model at present. Meanwhile, the Hubble tension between the local measurement of H 0 and model dependent H 0 remains unsolved. Therefore, in the future, more comprehensive observation and analysis are needed to obtain more effective solutions for current issues and more robust conclusions.