Holographic complexity growth in a FLRW universe

TL;DR

This paper explores how holographic complexity grows in a FLRW universe by analyzing two models derived from AdS-Schwarzschild geometry, revealing contributions from interactions and volume changes, with results depending on the realization method.

Contribution

It introduces two methods to realize FLRW universes holographically and compares their effects on complexity growth, highlighting differences between complexity-volume and complexity-action approaches.

Findings

Complexity growth includes interaction and volume change contributions.

Volume law dominates the divergence in complexity growth rate.

Discrepancies between CV and CA conjectures in closed universe case.

Abstract

We investigate the holographic complexity growth rate of a conformal field theory in a FLRW universe. We consider two ways to realize a FLRW spacetime from an Anti-de Sitter Schwarzschild geometry. The first one is obtained by introducing a new foliation of the Schwarzschild geometry such that the conformal boundary takes the FLRW form. The other one is to consider a brane universe moving in the Schwarzschild background. For each case, we compute the complexity growth rate in a closed universe and a flat universe by using both the complexity-volume and complexity-action dualities. We find that there are two kinds of contributions to the growth rate: one is from the interaction among the degrees of freedom, while the other one from the change of the spatial volume of the universe. The behaviors of the growth rate depend on the details to realize the FLRW universe as well as the holographic conjecture for the complexity. For the realization of the FLRW universe on the asymptotic boundary, the leading divergent term for the complexity growth rate obeys a volume law which is natural from the field theory viewpoint. For the brane universe scenario, the complexity-volume and complexity-action conjectures give different results for the closed universe case. A possible explanation of the inconsistency when the brane crosses the black hole horizon is given based on the Lloyd bound.