Determination of H 0 $H_{0}$ and r d $r_d$ in Horava–Lifshitz Gravity Using DESI-Y1 and SDSS-IV Dataset: Alleviating the Hubble Tension

Observational data are used from Baryon Acoustic Oscillations (DESI-Y1 and SDSS-IV), the ${\text{Pantheon}}^{+}$ 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 ($H_0$), the sound horizon ($r_d$), and the running parameter $\lambda$ is extracted, which governs the flow between the UV and Infra-Red (IR) regimes. By treating $r_d$ as a free parameter, this approach remains independent of early-Universe and recombination assumptions. These analysis yields $H_0=71.1_{-1.7}^{+1.5}\text{km}{s}^{-1}{\text{Mpc}}^{-1}$, suggesting that the HL gravity model alleviates the Hubble tension, reducing the discrepancy from more than $4.89\sigma$ (between Planck and Riess) to approximately $0.97\sigma$. Additionally, the model predicts ${\Omega }_{m0}=0.2803$, in alignment with values reported by the DESI-Y1, and $r_d=146.6\pm 2.4\text{Mpc}$, which is in close agreement with the value predicted by the Planck collaboration. The spatial curvature parameter is ${\Omega }_{k0}=0.0210$, consistent with predictions from the Wilkinson Microwave Anisotropy Probe (WMAP), suggesting a flat Universe. Additionally, the running parameter $\lambda$ is constrained to lie near its IR limit ($\lambda =1.1439\pm 0.0098$), 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 $\Lambda \text{CDM}$ model using various Statistical Metrics.