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) $SO(1,4)\to SO(1,3)$, driven by a Higgs field $Φ$ 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 $θ$-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 $\langle Φ\rangle = v_1$ 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 $ Λ<em>1 &gt; \cdots &gt; Λ_k &gt; \cdots$, where the Cosmological Constant decreases monotonically toward the asymptotic attractor $Λ</em>\infty = 0$.