Comparative Analysis Between the 5D τ -Delay Field Model and Gupta's CCC+TL Cosmology: Demonstrating the 4D Limit of a Unified Delay-Geometry Framework

This short comparative paper shows that the “CCC+TL Cosmology” proposed by Rajendra P. Gupta in Galaxies (2025) is mathematically equivalent to the four-dimensional limit of the 5D tau-Delay Field (TDF) model previously introduced by Bahman Masarrat in Integrating a 5D Scalar Field with General Relativity and Photonic Contributions (Zenodo DOI: 10.5281/zenodo.16734846).

While Gupta’s model explains cosmic acceleration and galaxy rotation without dark matter or dark energy by assuming a gradual weakening of the Universe’s forces, the TDF model derives the same effects naturally from geometric time-delay dynamics in an extra compact dimension.

This publication documents the theoretical relationship between the two models and highlights that Gupta’s formulation can be viewed as a simplified four-dimensional projection of the more complete TDF framework. The note establishes prior theoretical development and clarifies the deeper geometrical origin of the effects attributed to changing fundamental constants.