Relativity and Cosmology

    

Haar Measure on Spacetime as Geometric Source of Dark Energy

Authors: Vladimir Trifonov, Philip V. Trifonov

We present a model of a purely geometric source of Dark Energy (effective cosmological constant) within the framework of Hyperhamiltonian Quantum Mechanics where spacetime acquires a locally compact Lie group structure with two volume measures (Haar, generated by the multiplication on the group, and Lebesgue, induced by the natural closed FLRW metric of the group). Following earlier suggestion by one of the authors that the group-invariant Haar measure may address non-Newtonian behavior at large scales, it is taken to represent vacuum energy density, while Lebesgue is assumed responsible for matter/radiation density. It is shown that Haar vacuum energy mimics dark energy at cosmological scales, generating accelerated expansion geometrically without an explicit cosmological constant. We develop a self-contained linear cosmological perturbation theory to show almost perfect agreement with LambdaCDM.

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[v1] 2026-04-04 18:58:40

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