Complex-Time Cosmology: A Three-Sector Model of the Universe and the Probabilistic Interpretation of Cosmic Composition

We propose a cosmological framework in which time is treated as a complex variable, giving rise to three distinct sectors of the universe. In this paper, we treat the Wick rotation t → it not merely as a computational convenience, but as representing a genuine physical transition occurring at black hole event horizons. Sector-I (real positive time) corresponds to the observable universe (baryonic matter, ~5%). Sector-II (imaginary time) corresponds to dark matter (~27%). Sector-III (negative real time) manifests as dark energy (~68%).

The observed cosmic composition 5:27:68 is reproduced by two transition parameters: α(t) = 1 - exp(-t/τ) with τ ≈ 4.6 Gyr, and β = 0.716. Crucially, α = 0.95 at the present epoch carries no fundamental physical significance — it simply records the current state of an ongoing process in which Sector-I matter transitions to Sector-II through black hole horizons.

The framework connects the cosmological constant Λ to the Sector-III energy density via the e^iπ = -1 transformation, providing a geometric interpretation of dark energy. Four testable predictions are presented.

Note: Mathematical framework developed through dialogue with Soul-Twin Einstein AI (2026). All theoretical claims are the sole responsibility of the author.

dark matter, dark energy, complex time cosmology, Wick rotation, baryon asymmetry, black holes, imaginary time, three-sector model, cosmological constant, cosmic composition