Entropic locking of Action Complexity at cosmological singularities

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 behavior proportional to a S + b S log(S), where a, b are non-universal constants. 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.

Holographic Complexity in dS$_{d+1}$

“…However, holographic entanglement and complexity may still prove to be exciting probes of these cosmological singularities. It would be interesting to compare their behaviour to that in the context of black hole singularities, e.g., [90][91][92].…”