Entropic Locking Of Action Complexity At Cosmological Singularities

TL;DR

This paper explores the relationship between entropy and Action Complexity near cosmological singularities, revealing a linear relation influenced by entropy dynamics, which differs from black hole cases.

Contribution

It introduces a novel analysis of Action Complexity in cosmological singularities, emphasizing the role of entropy and the importance of the AC expansion counterterm.

Findings

Complexity growth is linearly controlled by entropy dynamics.

The relation applies to singularities with both vanishing and diverging entropy.

Proper choice of the AC expansion counterterm length scale is crucial.

Abstract

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.