Symmetric Time Approach: Reinterpreting Cosmic Inflation and Dark Energy via Temporal Divergence at Absolute Rest

This paper presents a unified solution to the two overarching crises of contemporary cosmology
— inflation physics and the nature of dark energy — without introducing hypothetical scalar fields
or exotic constants, modifying solely elementary relativistic kinematics. We propose a symmetric
extension of the Lorentz factor wherein the flow of time asymptotically diverges to infinity both at
the ultra-relativistic limit (v → c) and at the absolute rest limit (v → 0), anchored to the cosmic
microwave background rest frame. Under this Symmetric Time Approach (STA), the primordial
inflationary phase is described as an automatic “temporal inflation” emerging from the initial state
of rest, providing the universe with the necessary span to achieve thermal equilibrium and resolve
the Horizon Problem before the onset of material motion. Analogously, we demonstrate that current
cosmic acceleration emerges as a kinematic optical-temporal illusion: as the universe expands and
the mean macroscopic velocity of matter decays, the corresponding acceleration of the observer’s
local clock distorts astronomical distance measurements, mimicking the signature of a positive cosmological constant. The model is kinematically consistent, preserves classical Special Relativity in
high-energy regimes, and yields testable quantitative predictions via redshift drift anomalies at high
redshifts (z > 3).