Nucleation of de Sitter from the anti de Sitter spacetime in scalar field models

We show that, in the framework of Einstein-scalar gravity, the gravitational coupling can drive the nucleation of the de Sitter (dS) spacetime from an anti de Sitter (AdS) one. This is done using a static and spherically-symmetric metastable scalar lump solution. This features an $\text{AdS}_4$ spacetime in the solution's core, allows for $\text{dS}_4$ vacua and is plagued by a tachyonic instability. Using the Euclidean action formalism in the semiclassical approximation, we compute and compare the probability amplitudes and the free energies of the $\text{AdS}_{4}$ lump and the $\text{dS}_4$ vacua. Our results show that the former is generally less favored than the latter, with the most preferred state being a $\text{dS}_4$ vacuum. Thus, we interpret the lump as a metastable state which mediates the decay of the $\text{AdS}_4$ spacetime into the true $\text{dS}_4$ vacuum. We argue that this nucleation mechanism of dS spacetime may provide insights into the short-distance behavior of gravity, in particular for the characterization of supergravity vacua, cosmological inflation and the black-hole singularity problem.