Beyond $\Lambda$CDM with a Logistic RG-like Flow of the Low Redshift Cosmic Evolution

Recent cosmological observations show hints for possible deviations from the standard $\Lambda$CDM paradigm at late times. To study such deviation, we introduce a minimal phenomenological framework in which the total equation of state of the Universe, $w_{\rm T}(z)$, follows a logistic evolution motivated by a renormalization group like flow between cosmological fixed points. This approach directly reconstructs $w_{\rm T}(z)$ probed by background observables, without assuming a specific dark energy model. Using DESI-DR2 baryon acoustic oscillation measurements, DES-Dovekie latest supernova data, and CMB distance priors, we find that the logistic parametrization provides an improved fit compared to $\Lambda$CDM and remains competitive with standard dynamical dark energy models. The inferred expansion history exhibits noticeable deviations from $\Lambda$CDM at low redshifts, reflected in the reconstructed jerk parameter. While the statistical significance of these deviations is model-dependent, our results highlight the potential of flow-inspired parametrizations as a complementary and physically interpretable framework for probing late-time cosmic dynamics.