Constraining $Λ$CDM, $ω$CDM, and $ω_0ω_a$CDM models with DESI DR2 BAO: Redshift-Resolved Diagnostics and the Role of $r_d$

We present a detailed comparison of $Λ$CDM, $ω$CDM, and $ω_0ω_a$CDM cosmologies using the latest redshift-resolved BAO measurements from DESI DR2. By separating $r_d$-dependent and $r_d$-independent observables and applying both fixed and model-derived sound horizon values, we test the consistency of each model across 24 observables spanning redshift 0.2 to 2.3. Our results show that the $ω$CDM model is statistically favored over $Λ$CDM, with lower $χ^2$, AIC, and BIC values and reduced residuals, especially at $z = 0.706$ and 0.934. In contrast, the $ω_0ω_a$CDM model is strongly disfavored, even when using model-specific $r_d$, due to large residuals caused by the unphysical high-redshift behavior.