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

M. Cadoni; M. Pitzalis; A. P. Sanna

doi:10.1140/epjc/s10052-025-13960-1

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 227
https://doi.org/10.1140/epjc/s10052-025-13960-1

Regular Article - Theoretical Physics

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

M. Cadoni¹^,2, M. Pitzalis¹^,2^a and A. P. Sanna¹^,2

¹ Dipartimento di Fisica, Università di Cagliari, Cittadella Universitaria, 09042, Monserrato, Italy
² I.N.F.N, Sezione di Cagliari, Cittadella Universitaria, 09042, Monserrato, Italy

^a mirko.pitzalis@ca.infn.it

Received: 15 January 2025
Accepted: 17 February 2025
Published online: 5 March 2025

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 ${AdS}_{4}$ $\text {AdS}_4$ spacetime in the solution’s core, allows for ${dS}_{4}$ $\text {dS}_4$ 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 ${AdS}_{4}$ $\text {AdS}_{4}$ lump and the ${dS}_{4}$ $\text {dS}_4$ vacua. Our results show that the former is generally less favored than the latter, with the most preferred state being a ${dS}_{4}$ $\text {dS}_4$ vacuum. Thus, we interpret the lump as a metastable state which mediates the decay of the ${AdS}_{4}$ $\text {AdS}_4$ spacetime into the true ${dS}_{4}$ $\text {dS}_4$ 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.

© The Author(s) 2025

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