Complex time as a unified geometric structure: from quantum coherence to cosmological dynamics(UT1)

We propose a unified geometric framework in which physical time is described by a complex variable T=t−iτ, whose real component determines causal structure while the imaginary component encodes an internal temporal degree of freedom. Building on recent results showing that the imaginary part τ governs quantum coherence in interferometric experiments and simultaneously generates dark-energy and dark-matter phenomenology in cosmology, we show that both regimes arise from the same bidimensional temporal geometry. In the quantum domain, rotations in the internal (t,τ) plane reproduce the visibility variations observed in Wheeler-type delayed-choice experiments without invoking retrocausality, and correspond operationally to CP-TP dephasing channels. In the cosmological domain, the dynamics of τ(t) contribute an effective energy density and pressure driving late-time acceleration, while spatial gradients ∇τ generate an effective gravitational density ρeff∝(∇τ)2 that yields isothermal halo profiles and asymptotically flat rotation curves. We argue that these two manifestations—quantum coherence and dark-sector phenomenology—are not independent, but reflect a single geometric structure of time. The complex temporal plane thus provides a minimal and covariant mechanism linking interference, cosmic acceleration, and galactic dynamics, suggesting that the dark sector and quantum attenuation may share a common origin in the internal geometry of time.