Emergent cosmic time as a phenomenological interpretation of the Hubble tension in the MBD framework

The discrepancy between the locally inferred Hubble constant and the value reconstructed from the cosmic microwave background within ΛCDM remains one of the main tensions in late-time cosmology. This work explores the hypothesis that the effective time experienced by cosmic clocks differs from the coordinate time of the FLRW metric. A minimal phenomenological implementation, inspired by the broader MBD framework, is parameterized through a redshift-dependent emergent-time factor N(z), such that dt_eff = N(z) dt and H_eff(z) = H_t(z)/N(z). Several families for N(z) are explored numerically; a refined scan in the sigmoid family yields 185 simultaneously validated models and identifies a stable compatible region around N0 ≈ 0.916–0.920, z_c ≈ 0.045–0.070, w ≈ 0.010–0.030. The main prediction is an effective present‑day deceleration parameter q_eff,0 ≈ –0.75 ± 0.14, significantly more negative than the standard ΛCDM value (–0.55), yet physically plausible and falsifiable. This framework offers an alternative interpretation of the Hubble tension without introducing exotic matter components.