A Unified Field Theory of Emergent Geometry and Cyclic Cosmology

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.