Recurrent Universe: Asymptotic Linearization through Energy Transitions

The ΛCDM model predicts accelerated expansion driven by dark energy with , below the threshold . This article interprets the asymptotic suppression of the dynamical gravitational term in Friedmann cosmology as signaling a geometrically degenerate limit corresponding to a linear configuration. Thus, geometric evolutionary extension is introduced in which effective spatial degrees of freedom become dynamically suppressed while metric isotropy is preserved. Challenges—matter dominance over antimatter and the absence of annihilation radiation—are addressed by a finite dark energy (DE) flat interface separating m–m̄ domains, embedded in a spatially flat geometry (Ω_tot≃1). Progressive thinning of the interface supports the dark energy density responsible for accelerated expansion. When the interface is fully extinguished, gravitational convergence and maximal annihilation enforce dynamic dimensional reduction. This reduced geometry yields , corresponding to a symmetric energetic configuration that reaches maximum dark-energy density in the linear state of maximal expansion defined by the separation of two residual excitations. This limit satisfies an effective self-neutralization condition , where is defined operationally from the Friedmann dynamics, with vanishing kinetic contribution and a degenerate curvature structure. The resulting boundary state enables linear dark energy–mass duality and cyclic regeneration of three-dimensional space. This work aims to explore a correspondence between the linear state of maximal expansion and the state of maximal contraction through a dynamical dimensional transition consistent with the second law of thermodynamics. It is not an alternative to ΛCDM but a natural extension of its asymptotic boundary states.