Author's Note to Version 2 (Major Revision) This Version 2 introduces mathematical corrections and significant expansions to the original theoretical framework, although the core phenomenological hypothesis—exploring cosmic evolution without dark energy via spacetime scale transformation—remains the primary focus. Key Changes and Additions: The notation for the spacetime projection scale factor has been updated from (z) to K (z) throughout the manuscript. Major Revision in Section 4 (Luminosity Distance Derivation): The mathematical derivation of the luminosity distance has been restructured. The new derivation natively incorporates the gradient of the spacetime scale directly into the propagation path of light, establishing a new effective comoving distance formula. Significant Expansion in Section 4. 2 (Cosmic Age Re-calculation): Previously only briefly mentioned, the section regarding absolute time in the early universe has been substantially expanded. It now includes explicit integral calculations for the projected cosmic age (tₑ₎₉), suggesting that the local physical time at z=8 could extend to approximately 3. 6 Gyr. Additions to Section 3: Expanded the theoretical explanation regarding the multiscale spacetime postulate and the local derivative separation rule to reinforce its phenomenological foundation in general relativity. New Appendix (Appendix B): Added a new mathematical verification framework to examine the relative change rate of the scale factor K (z) under local time coordinate transformations. Abstract Modern standard cosmology (CDM) introduces dark energy to explain the accelerated expansion of the universe; however, recent discoveries of massive early galaxies by the James Webb Space Telescope (JWST) (Labbé et al. , 2023) call for alternative interpretations of existing cosmological observation scales. Building upon a prior study (Kim, 2026) that proposed a dimensionless expansion rate coefficient combining the amount of cosmic expansion and the flow of time, this study proposes a phenomenological spacetime projection scale factor K (z) based on the constancy of the speed of light. Specifically, to reduce the possibility of geometric distortion in observation scales, we adopt the matter-dominated Einstein-de Sitter (EdS) universe model (ₘ=1) as the theoretical baseline, and derive new effective comoving distance and luminosity distance formulas by internalizing the gradient of the spacetime scale directly into the propagation path of light. Applying the newly derived luminosity distance to supernova observational data (Scolnic et al. , 2022) suggests a high level of model degeneracy, closely matching the standard CDM model in the low-redshift (z<1. 0) range. Conversely, in the deep space (z=8. 0) region, it exhibits a distance modulus deviation of +0. 78 mag; through the cosmic age integration reflecting the projection factor, it is hypothesized that the local physical time at that epoch is significantly extended compared to prior predictions. Consequently, this study suggests that the phenomenon previously interpreted as dark energy by existing models might actually be a geometric illusion of the spacetime scale, thereby exploring an economical geometric hypothesis that can simultaneously explain the evolutionary curve of the universe and the securing of absolute time in the early universe without introducing unknown energy.
Sun-gyu Kim (Mon,) studied this question.