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Abstract

We present a comparative statistical analysis of two Dirac--Born--Infeld (DBI) type k-essence scalar field models (Model I and Model II) for late-time cosmic acceleration, alongside the standard $\Lambda$CDM and $w$CDM benchmarks. The models are constrained using a joint dataset comprising Pantheon+, Hubble parameter measurements, and Baryon Acoustic Oscillation (BAO), including the latest DESI DR2 release. To ensure efficient and accurate likelihood evaluations, we employ Bayesian inference via Markov Chain Monte Carlo (MCMC) with the No-U-Turn Sampler (NUTS) in \texttt{NumPyro}, supplemented with a machine learning (ML) emulator. Model selection is performed using the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). The results demonstrate excellent consistency between the MCMC and ML emulator approaches. Compared to the reference models, $\Lambda$CDM and $w$CDM, Model I yields the lowest $\chi^2$ and a negative $\Delta$AIC relative to $\Lambda$CDM, indicating a mild statistical preference for its richer late-time dynamics, though the BIC penalizes its additional parameter and prevents a decisive advantage. Conversely, Model II has a lower accuracy compared to both $\Lambda$CDM and $w$CDM according to AIC and BIC, leading to its disfavor. Notably, Model I also delivers $H_0=73.67\pm0.15$ (without the nuisance parameter $\mu_0$) in agreement with SH0ES, and $H_0=69.65\pm0.83$ (with $\mu_0$) as an intermediate value, thereby reconciling with local measurements while simultaneously providing a compromise between early and late universe determinations. This dual feature offers a promising pathway toward alleviating the Hubble tension. Overall, our analysis highlights the significance of non-canonical scalar field models as viable alternatives to $\Lambda$CDM and $w$CDM, which often provide improved fits to current observational data.