Relativity and Cosmology

Regularization of Cosmological Singularities, CPT Symmetry, and the Geometric Origin of Mass in Complex Time with a Planckian Floor

Authors: Hidehito Koseki

This paper proposes a theoretical framework that redefines time as a complex variable with a fixed imaginary constant floor, z=tpm it_{P} (where t_{P} is the Planck time), operating across all cosmological epochs. This approach aims to reconcile the avoidance of cosmological singularities with the consistency of physical laws in the macroscopic universe. Although traditional approaches introducing imaginary time—such as the Hartle—Hawking no-boundary proposal—successfully addressed the Big Bang singularity at t=0, their application was largely restricted to local Wick rotations in the early universe to avoid causality violation and non-unitary dynamics in macroscopic domains. Here, rather than treating the imaginary component as a dynamical degree of freedom, we introduce it as a fixed lower bound (Im-floor) corresponding to an intrinsic limit of temporal resolution. This formulation smoothly recovers standard physics in the macroscopic limit (tgg t_{P}) while offering unified geometric interpretations for three fundamental phenomena: (1) full regularization (C^{infty } continuity) of the cosmological origin (t=0) through a contour bypass in the complex plane, thereby avoiding the classical singularity; (2) direct correspondence between the sign of the imaginary component (pm it_{P}) and CPT conjugation, mapping matter (+it_{P}) and antimatter (-it_{P}) to dual phase domains; and (3) a geometric representation of rest mass versus masslessness as the presence (text{Im},z=pm t_{P}) or absence (Imu2009z=0) of an "imaginary temporal width" in complex spacetime. This model provides a concise, unified geometric perspective on foundational issues at the intersection of cosmology, quantum field theory, and particle physics.

Comments: 11 Pages.

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Submission history

[v1] 2026-10-26 02:38:05

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