Coleman-de Luccia Tunneling in a Metastable Φ6 Potential: Numerical Instantons and the Prime Field Instability

We propose and numerically analyze a model of open inflation originating from the quantum decay of a metastable "Prime Field," Φ, with a Φ⁶-tilted double-well potential, V(Φ) = (λ/4)(Φ² - ν²)² + (κ/M_P²)Φ⁶. The Φ⁶ term creates a false vacuum at Φ = 0, whose decay via a Coleman-de Luccia (CdL) instanton naturally initiates an inflationary epoch. We present a comprehensive numerical study of the CdL instanton solutions using a shooting method with O(4) symmetry across the parameter space 0.01 < α < 0.9, where α = (4κν²)/(λM_P²) controls the vacuum energy splitting. Our results chart the smooth transition from thick-wall to thin-wall regimes, with the Euclidean action decreasing from B ≈ 42.8 to B ≈ 2.9. This numerical framework and the computed instanton profiles establish the necessary foundation for calculating the primordial perturbation spectra and predicting a tensor-to-scalar ratio in the observationally relevant range 0.05 ≤ r ≤ 0.1.