A Unified Interpretation of Supernova, GRB, and QSO Time Dilation Signals in a Generalized Cosmological Time Framework

Abstract

Cosmological time dilation (CTD) serves as a fundamental probe of cosmic expansion, historically verified through the characteristic (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 interred 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. We 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_{\rm obs} \propto (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_{\rm intr} \propto (1+z)^{-2}) that masks the cosmological signal. This framework reconciles the diverse behaviors of transient and persistent sources without modifying local physical laws.

Figures (2)

• Figure 1: Schematic representation of the unified GCT interpretation for three classes of cosmic clocks. Top & Middle: SNe Ia and GRBs originate from shielded, gravitationally bound progenitors. Their intrinsic timescales are fixed ($\tau_{\rm rest} = \text{const}$), so they act as standard clocks revealing the pure geometric path dilation $\tau_{\rm obs} \propto (1+z)^{1+b/4}$. Bottom: Quasars exhibit an apparent null result due to a selection effect. Fixed-wavelength observations probe inner, faster dynamical regions of the accretion disk at higher redshifts ($\tau_{\rm intr} \propto (1+z)^{-2}$), which effectively compensates the background time dilation signal.
• Figure 2: Conceptual comparison of the observed duration scaling with redshift for three source classes. The solid red line represents the pure cosmological time dilation ($\propto (1+z)^{1+b/4}$) exhibited by shielded clocks like SNe Ia. The scattered dots represent a schematic illustration of GRBs, which follow the same trend but with significant astrophysical noise. The blue dashed line shows the predicted scaling for QSOs, where the intrinsic selection effect ($\propto (1+z)^{-2}$) over-compensates the dilation, resulting in a net decreasing trend ($\propto (1+z)^{-1+b/4}$). (Here $b=0.04$ is assumed.)