Quantum relaxation dynamics of vacuum energy from pre-geometric gravity

Abstract We investigate a quantum relaxation mechanism for the vacuum energy density arising from the spontaneous symmetry breaking (SSB) $$SO(1,4)\rightarrow SO(1,3)$$ S O ( 1 , 4 ) → S O ( 1 , 3 ) , driven by a Higgs field $$\Phi $$ Φ in a MacDowell–Mansouri pre-geometric gravity framework. The theory predicts a countably infinite set of vacua, corresponding to distinct topological sectors, for a periodic Higgs potential with intervening barriers. This structure gives rise to a series of dualities and see-saw relations connecting fundamental scales – the Planck mass and the Cosmological Constant – to topological parameters such as the Gauss–Bonnet coupling and the $$\theta $$ θ -term, all of which emerge only after SSB. A striking consequence is the quantization of the vacuum energy into discrete levels. Starting from a vacuum expectation value $$\langle \Phi \rangle = v_1$$ ⟨ Φ ⟩ = v 1 associated with a large vacuum energy, the system evolves via quantum tunneling through the infinite landscape of minima. Crucially, we demonstrate that the transition probability is maximized for the ordered sequence $$ \Lambda _1> \cdots> \Lambda _k > \cdots $$ Λ 1 > ⋯ > Λ k > ⋯ , where the Cosmological Constant decreases monotonically toward the asymptotic attractor $$\Lambda _\infty = 0$$ Λ ∞ = 0 .