Constraining a generalized ΛCDM model with cosmic chronometers, supernovae, and DESI BAO data

We investigate a generalized $\Lambda$CDM cosmological model defined by a modified expansion rate given by $H\left(z\right)=H_0\sqrt{\alpha {(1+z)}^n+(1-\alpha )}$, where the additional parameter $n$ governs the redshift dependence of the matter contribution. We perform a comprehensive statistical analysis using progressively richer observational datasets, including cosmic chronometers (CC), the PantheonPlus and SH0ES supernova samples (PP+SH0ES), and DESI BAO measurements. The resulting posterior constraints demonstrate that adding late-time probes systematically tightens the allowed parameter ranges and shifts the best-fit $H_0$ toward the local SH0ES estimate, while remaining consistent with CC constraints. We find that the generalized $\Lambda$CDM model provides excellent agreement with both $H\left(z\right)$ and distance modulus data, yielding reduced ${\chi }_{\text{red}}^2$ values close to unity across all dataset combinations. Information criteria (AIC and BIC) analyses show weak support for the additional parameter with CC alone but strong evidence for its inclusion when PP+SH0ES and DESI data are combined. The evolution of key dynamical quantities, such as the energy density, deceleration parameter $q\left(z\right)$, and total equation of state (EoS) $\omega \left(z\right)$, further confirms the model’s physical viability, with present-day values of $q_0\approx -0.563$ and ${\omega }_0\approx -0.709$, indicating a mildly accelerating universe.