Vacuum stability in Geometric Trinity of Gravity

Abstract

We investigate whether the classical equivalence of general relativity, its teleparallel equivalent, and its symmetric teleparallel equivalent extends to false-vacuum decay at leading semiclassical order. For a real scalar field minimally coupled to gravity, we compare the tunnelling exponent $B=S_{\mathrm{b}}-S_{\mathrm{fv}}$, which determines the exponential suppression of the decay rate, $\Gamma \sim e^{-B}$, with the Euclidean bounce, $S_{\mathrm{b}}$, and false-vacuum actions, $S_{\mathrm{fv}}$. The three formulations admit the same $O(4)$-symmetric Coleman-De Luccia bounce, but the boundary terms relating their actions can contribute to $B$. We explicitly evaluate the torsion and non-metricity boundary contributions at the regular origin, $r=0$, and at the asymptotic endpoint, $r\to \infty$. For regular configurations with consistently matched bounce and false-vacuum boundary data, these contributions vanish in both TEGR and STEGR. We therefore obtain $B_{\mathrm{GR}}=B_{\mathrm{TEGR}}=B_{\mathrm{STEGR}}$, establishing that the three formulations predict the same leading semiclassical suppression of false-vacuum decay within the class of configurations and boundary conditions considered.

arXiv comment30 pages, 1 figures