Λ( t )CDM model: cosmological implications and dynamical system analysis*

Abstract We investigated a time-varying cosmological constant model using recent BAO measurements from DESI DR2, combined with Type Ia supernova samples (Pantheon , DES-Dovekie, and Union3) and CMB shift parameters, to constrain the CDM model parameters via Markov Chain Monte Carlo analysis. We find that the interaction term Q ( z ) shows a sign change for all dataset combinations by crossing Q ( z )=0, depending on the choice of the dataset: at low redshift, Q ( z )0, corresponding to dark matter decaying into vacuum energy. The dynamical system analysis found three critical points, namely, , and . The resulting critical points, determined by the underlying cosmological parameters, correspond to distinct epochs in cosmic evolution. Depending on the parameter combinations, these points characterize various cosmological phases, ranging from an accelerated stiff matter-dominated era to late-time accelerated expansion. The stability of each critical point is analyzed using linear stability theory, with the relevant physical constraints on the cosmological parameters duly incorporated throughout the analysis. For each dataset combinations, the CDM model predicts that , showing a preference for dynamical dark energy over the cosmological constant scenario with . Consequently, the model exhibits a transition phase in the range to −0.48 and predicts in the range −0.54 to −0.52, with the precise transition point depending on the choice of dataset. Finally, the Bayesian evidence shows strong support for the CDM model over ΛCDM.