A Unified Field Theory of Emergent Geometry and Cyclic Cosmology

Abstract We propose a unified field theory of emergent geometry and cyclic cosmology, developed within the framework of Information Connectivity Theory (ICT). In this framework, spacetime, gravity, and matter emerge from the dynamics of a primordial information network. The theory posits a fundamental field s(x,t)s(x,t)—the entropy of causal connectivity—representing the local density of causal connections between events. Spacetime geometry arises as a macroscopic approximation of the network's connectivity structure, and gravity is interpreted as the system's response to minimize topological stress—specifically, the risk of global disconnectivity. We introduce a complete action principle with a saturating potential, derive the stochastic field equations governing the dynamics of ss, and demonstrate that the spacetime metric emerges as the statistical correlation of its gradients: gμν=⟨∂μs∂νs⟩gμν=⟨∂μs∂νs⟩. We show that ICT provides a rigorous first-principles derivation of the phenomenological Elastic Cyclical Cosmology (ECC) Gimranov, 2025a, recovering its key equations and concepts—spacetime elasticity, the active role of dark matter, the Gimranov limit, and cyclical rebirth—as emergent macroscopic properties. Furthermore, ICT offers a natural foundation for quantum mechanics as the statistical mechanics of the underlying discrete network, provides a topological interpretation of black holes, and generates new testable predictions for cosmology and high-energy physics.