Determination of H0$H_{0}$ and rd$r_d$ in Horava–Lifshitz Gravity Using DESI‐Y1 and SDSS‐IV Dataset: Alleviating the Hubble Tension

Abstract Observational data are used from Baryon Acoustic Oscillations (DESI‐Y1 and SDSS‐IV), the sample, and Cosmic Chronometers measurements to constrain key cosmological parameters within the framework of Hořava‐Lifshitz (HL) gravity. Specifically, the posterior distribution of Hubble constant (), the sound horizon (), and the running parameter is extracted, which governs the flow between the UV and Infra‐Red (IR) regimes. By treating as a free parameter, this approach remains independent of early‐Universe and recombination assumptions. These analysis yields , suggesting that the HL gravity model alleviates the Hubble tension, reducing the discrepancy from more than (between Planck and Riess) to approximately . Additionally, the model predicts , in alignment with values reported by the DESI‐Y1, and , which is in close agreement with the value predicted by the Planck collaboration. The spatial curvature parameter is , consistent with predictions from the Wilkinson Microwave Anisotropy Probe (WMAP), suggesting a flat Universe. Additionally, the running parameter is constrained to lie near its IR limit (), indicating a restoration of Lorentz invariance at cosmological scales and a behavior close to General Relativity. The viability of the Hořava–Lifshitz model is evaluated in comparison to the standard model using various Statistical Metrics.

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