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

Abstract 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 $$\text {AdS}_4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>AdS</mml:mtext> <mml:mn>4</mml:mn> </mml:msub> </mml:math> spacetime in the solution’s core, allows for $$\text {dS}_4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>dS</mml:mtext> <mml:mn>4</mml:mn> </mml:msub> </mml:math> 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 $$\text {AdS}_{4}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>AdS</mml:mtext> <mml:mn>4</mml:mn> </mml:msub> </mml:math> lump and the $$\text {dS}_4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>dS</mml:mtext> <mml:mn>4</mml:mn> </mml:msub> </mml:math> vacua. Our results show that the former is generally less favored than the latter, with the most preferred state being a $$\text {dS}_4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>dS</mml:mtext> <mml:mn>4</mml:mn> </mml:msub> </mml:math> vacuum. Thus, we interpret the lump as a metastable state which mediates the decay of the $$\text {AdS}_4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>AdS</mml:mtext> <mml:mn>4</mml:mn> </mml:msub> </mml:math> spacetime into the true $$\text {dS}_4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>dS</mml:mtext> <mml:mn>4</mml:mn> </mml:msub> </mml:math> 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.