Late-Time Cosmic Acceleration in Ho\v{r}ava-Lifshitz Gravity: Observational Evidence from Cosmic Chronometers and Pantheon+SHOES Datasets
We investigate the cosmological implications of Horava-Lifshitz (HL) gravity using a redshift-dependent deceleration parameter of the form $q(z) = q_0 + \frac{q_1 \ln(1+z)}{1 + n\ln(1+z)}$, from which the Hubble parameter $H(z)$ is derived analytically. This parametrization captures the transition from early deceleration to late-time acceleration, with a logarithmic correction governed by $n$ that distinguishes it from standard kinematic models. Model parameters $H_0$, $q_0$, $q_1$, and $n$ are constrained via MCMC using cosmic chronometer (CC) and Pantheon+SHOES datasets, individually and in combination. Across all dataset combinations, $q_0 < 0$, confirming ongoing accelerated expansion. The reconstructed $H(z)$ is consistent with $\Lambda$CDM at low redshifts, with mild deviations at higher redshifts. The $\{r, s\}$ statefinder parameters indicate that the model evolves smoothly, beginning with Chaplygin gas-type behaviour, crossing the $\Lambda$CDM fixed point, and settling into a quintessence-like phase at late times. The $Om(z)$ diagnostic reveals negative slopes throughout, indicating quintessence-like dark energy ($w > -1$). Present-day cosmic age estimates from the individual and combined datasets yield $t_0 \approx 13.7$ Gyr, in agreement with Planck 2018 constraints.