Entropic locking of Action Complexity at cosmological singularities

• Published in: The journal of high energy physics 2020-04, Vol.2020 (4), p.1-22, Article 11
• Main Authors: Barbón, J.L.F., Martín-García, J.
• Format: Article
• Language: English
• Subjects: AdS-CFT Correspondence; Black Holes; Black Holes in String Theory; Classical and Quantum Gravitation; Complexity; Domains; Elementary Particles; Entropy; High energy physics; Locking; Models of Quantum Gravity; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity; Relativity Theory; Singularities; String Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP04(2020)011

A bstract We study the relation between entropy and Action Complexity (AC) for various examples of cosmological singularities in General Relativity. The complexity is defined with respect to the causal domain of dependence of the singular set, and the entropy is evaluated on the boundary of the same causal domain. We find that, contrary to the situation for black hole singularities, the complexity growth near the singularity is controlled by the dynamics of the entropy S , with a characteristic linear relation. This formula is found to apply to singularities with vanishing entropy as well as those with diverging entropy. In obtaining these results it is crucial to take into account the AC expansion counterterm, whose associated length scale must be chosen sufficiently large in order to ensure the expected monotonicity properties of the complexity.