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

TL;DR

This paper presents a unified interpretation of supernova, GRB, and QSO time dilation signals within a generalized cosmological time framework, resolving previous discrepancies by distinguishing between geometric clocks and thermal emission effects.

Contribution

It introduces a novel framework that explains the differing time dilation observations by separating global coordinate time from local proper time, accounting for environmental shielding and intrinsic selection effects.

Findings

Supernova and GRB time dilation signals are consistent with geometric path dilation.

Quasar observations are explained by intrinsic selection effects masking cosmological signals.

The framework reconciles diverse observational behaviors without altering local physical laws.

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 \tau_{\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 (\tau_{\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.