Redefining Spacetime through the Cosmic Expansion Rate: Compatibility with Lorentz Transformations

This is the authors' abstract. We don't add key points for this paper.

This study proposes an alternative mathematical framework for describing the scales of time and space in terms of cosmic expansion, extending beyond the conventional treatment of expansion as a simple ratio of recession velocity to spatial distance. In standard cosmology, the Hubble constant (H_0) quantifies the expansion using independent baselines for time and length. In contrast, the proposed preliminary, hypothetical framework introduces a dimensionless spacetime-invariant parameter, termed the cosmic expansion coefficient (H_k) which directly relates cosmic expansion to the temporal flow. Based on the geometric constraints imposed by the constant speed of light (S=cT), temporal and spatial scales are geometrically constrained. Therefore, the relative variation (ratio) of the effective amount of cosmic expansion (U_exp) symmetrically synchronizes the spatial and temporal-flow scales, reflecting a physical causal relationship governed by a square-root factor. In this formulation, the invariance of H_k emerges naturally from the spacetime scale transformation rather than from an imposed assumption. Furthermore, this mechanism provides a mathematical basis for deriving formulae for time dilation, represented as a reduction in the infinitesimal temporal-flow scale, and spatial contraction, represented as a reduction in the infinitesimal spatial scale in special relativity. These transformations are expressed through geometric coupling of the temporal-flow and spatial scales, thereby providing a basis for examining their compatibility with the principles of special relativity.