Geometric Scalar Invariants as Dynamical Vacuum Energy: Coherence, Reheating, and the Cosmological Constant

We investigate a geometric scalar invariant of the form \(\:{\dot{\varphi\:}}^{2}{\varphi\:}^{2}\), motivated by energy–volume–frequency structures in relativistic particle systems. Embedded in a scalar field theory in FLRW spacetime, this term dynamically modulates energy density and coherence. We show that the invariant can support an inflationary phase, induce graceful exit without fine-tuned potentials, and decay as a power law, potentially explaining the current tiny dark energy scale. We then explore the field’s perturbation stability, reheating, quantum corrections, and radiative stability. Numerical simulations confirm that the invariant drives both inflationary behavior and a late-time vacuum-like energy component without requiring an unnaturally small cosmological constant. We discuss observational signatures, including the evolution of the expansion rate and growth of structure, and argue that upcoming surveys may constrain or detect this class of dynamical vacuum energy models.