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 AdS4 spacetime in the solution’s core, allows for dS4 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 AdS4 lump and the dS4 vacua. Our results show that the former is generally less favored than the latter, with the most preferred state being a dS4 vacuum. Thus, we interpret the lump as a metastable state which mediates the decay of the AdS4 spacetime into the true dS4 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.