A unified interpretation of supernova, GRB, and QSO time dilation signals in a generalized cosmological time framework

Cosmological time dilation (CTD) serves as a fundamental probe of cosmic expansion, historically verified through the characteristic $$(1+z)$$ ( 1 + z ) broadening of Type Ia supernova (SNe Ia) light curves. However, significant tensions arise when extending this test to other astrophysical regimes. While discrete, event-based transients such as gamma-ray bursts (GRBs) exhibit large scatter in inferred time-dilation signatures, analyses of stochastic variability in persistent sources – specifically quasars (QSOs) – frequently yield null results. I demonstrate that these discrepancies stem from a previously overlooked distinction between discrete geometric clocks and continuous thermal emission, presenting a resolution within the framework of generalized cosmological time (GCT). The central premise relies on strictly distinguishing global coordinate time, characterized by a generalized lapse function, from the local proper time measured within gravitationally bound systems. I propose that the progenitors of transients – specifically SNe Ia and GRB central engines – are effectively shielded from background time evolution due to strong gravitational binding and environmental decoupling. Consequently, they act as standard clocks tracing pure geometric path dilation, obeying τ ₒbs ∝ (1+z)1+b/4 τ obs ∝ ( 1 + z ) 1 + b / 4 . Conversely, the lack of dilation in QSOs is derived as a consequence of observing persistent thermal accretion disks at fixed wavelengths, introducing an intrinsic selection effect ( τ ᵢntr ∝ (1+z)⁻² τ intr ∝ ( 1 + z ) - 2 ) that masks the cosmological signal. This framework reconciles the diverse behaviors of transient and persistent sources without modifying local physical laws.