Emergent Inflation and Cosmological Perturbations from Graph Spectral Geometry

Presented is a minimal model in which spacetime, inflation, and primordial fluctuations emergefrom the dynamics of a discrete graph system. The fundamental degrees of freedom are encoded ina time-dependent adjacency matrix with a simple Hamiltonian governed by connectivity and acritical density parameter. Demonstrated is, that (i) a stable fixed point of the graph dynamicsinduces an inflationary phase, (ii) cosmological perturbations arise from fluctuations of the graphLaplacian spectrum, and (iii) the primordial power spectrum is directly determined by the spectraldensity of the graph. In the infrared limit, the model reproduces Einstein gravity via a spectralaction. Observable quantities such as the spectral index, its running, tensor modes, and non-Gaussianity are derived analytically and linked to geometric properties of the underlying graph. Theframework unifies aspects of discrete quantum gravity, renormalization group flows, and emergentspacetime.