Quintessence and false vacuum: Two sides of the same coin?

Abstract: We study late-time acceleration scenarios using a quintessence field initially trapped in a metastable false vacuum state. The false vacuum has non-zero vacuum energy and could drive exponential expansion if not coupled with gravity. Upon decay of the false vacuum, the quintessence field is released and begins to evolve. We assumed conditions where the effective scalar potential gradient must satisfy (\nabla V_{\text{eff}} > A), characterized by a pressure term approximately (\Delta p / p > \mathcal {O} (\hbar)) invoking the recently proposed string swampland criteria. We then derived the effective potential of the scalar with an upper bound on the coupling constant (\lambda < 0.6). Further analysis revealed that (V_{\text{eff}}) shows a slow-roll behavior for (0.1 > \lambda > -0.04) in the effective dark energy equation of state (EoS) (-0.8 < w_0 < -0.4), stabilizing at points between (1 < A < 2.718). Our results suggest a stable scalar decoupled from its initial meta-stable state, could indeed lead to a more stable universe at late times. However, slight deviations in parameter orders could potentially violate the swampland criteria if (V_{\text{eff}}) grows too rapidly. Since this is not something we expect, it opens up the possibility that the current dark energy configuration might be a result of a slowly varying scalar rather than being arbitrary. \