On AdS to dS transitions in higher-curvature gravity

We study the possible existence of gravitational phase transitions from AdS to dS geometries in the context of higher-curvature gravities. We use Lanczos-Gauss-Bonnet (LGB) theory with a positive cosmological constant as a toy model. This theory has two maximally symmetric vacua with positive (dS) and negative (AdS) constant curvature. We show that a phase transition from the AdS vacuum to a dS black hole geometry takes place when the temperature reaches a critical value. The transition is produced by nucleation of bubbles of the new phase that expand afterwards. We claim that this phenomenon is not particular to the model under study, that contains Boulware-Deser instabilities, but shall also be part of generic gravitational theories with higher-curvature terms, where these problems are absent. A salient feature that emerges when a positive cosmological constant is considered is that the temperature in which these bubbles may form is bounded from above. Thermodynamically this property is related to quite an uncommon feature that this system exhibits, namely, the existence of a zeroth-order phase transitionThe work of JDE and JASG is supported in part by MINECO (FPA2011-22594), Xunta de Galicia (GRC2013-024), the Spanish Consolider-Ingenio 2010 Programme CPAN (CSD2007- 00042) and FEDER. AG and JDE gratefully acknowledges support from FONDECYT (Chile) grant 1141309. JDE also wishes to acknowledge support from Marie Curie- IRSES/EPLANET, European Particle Physics Latin American Network, European Union 7th Framework Program, PIRSES-2009-GA-246806, and is thankful to the University of Buenos Aires, PUC Chile and UNAM Mexico for hospitality. AG wishes to thank the Theory Group of Santiago de Compostela for their hospitality. JASG acknowledges support from the Spanish FPI fellowship from FEDER grant FPA2011-22594S