Recurrent Universe: Asymptotic Linearization through Energy Transitions

This work is consistent with ΛCDM in the observable regime and investigates the asymptotic boundary structure associated with the states of maximal expansion and contraction of the Universe, including its relation to the accelerated expansion regime and preserving thermodynamic consistency (ΔS≥0).
Sócrates Georges Petrakis Mar 25, 2026

Sócrates Georges Petrakis      

Abstract

The standard ΛCDM cosmological model predicts accelerated expansion driven by dark energy (Λ), with w ≈ −1 , below the threshold w = −1/3 . This work examines the asymptotic suppression of the effective dynamical gravitational contribution (Epg) during global expansion in Friedmann cosmology—characterized by Ḣ → 0 —with the approach to a geometrically degenerate asymptotic regime. The observed dominance of matter (m) over antimatter (m̄ ) and the absence of large-scale annihilation radiation are interpreted through a finite dark-energy interface separating m and m̄ domains embedded in a three-dimensional spatial geometry consistent with Ωtot ≈ 1 . Progressive thinning of this interface sustains the dark-energy density driving accelerated expansion; the eventual extinction of the interface leads to gravitational convergence, maximal annihilation, and suppression of effective spatial degrees of freedom. This behavior is formalized within a geometric extension of the ΛCDM framework through spatial transitions in effective domains Φ(3D) → Φ(1D), preserving global  metric  isotropy.   The   resulting   boundary   configuration   satisfies E₀ + Epg = 0 , yielding a symmetric critical state where ρm = ρDE = ρm̄   at each point of the linear space, implying Tμν eff = 0 despite non-vanishing local energy density, with ρDE  denoting an effective linear dark-energy and E₀  the rest-energy  contribution. This state enables an effective energy–mass correspondence at maximal linear expansion and admits an equivalent representation as maximal contraction, which prevails as it is characterized by minimal residual dark energy. This process culminates in the dynamical regeneration of three-dimensional expansion, consistent with the second law of thermodynamics. The model is formulated not as an alternative to ΛCDM, but as a natural extension of its asymptotic boundary states.   

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