Krylov complexity of thermal state in early universe

TL;DR

This paper explores how Krylov complexity evolves in the early universe's thermal states, revealing exponential growth during inflation and saturation afterward, offering a quantum information perspective on cosmic evolution.

Contribution

It introduces a novel open-system approach using Krylov complexity to analyze thermal states across different early universe eras.

Findings

Krylov complexity grows exponentially during inflation.

Complexity saturates in RD and MD eras due to particle production.

The universe transitions from strongly to weakly dissipative regimes.

Abstract

Thermal interactions are ubiquitous in the cosmos, driving systems toward equilibrium. In this work, we investigate the evolution of thermal states across the early universe, encompassing the inflationary, radiation-dominated (RD), and matter-dominated (MD) eras, through the lens of Krylov complexity. Utilizing a purification scheme, we map the thermal state to a two-mode pure state, facilitating an open-system analysis of Krylov complexity in contrast to closed-system methodologies. Our numerical results demonstrate that Krylov complexity grows exponentially during inflation, indicating chaotic behavior, before saturating at nearly constant values in the RD and MD eras due to particle production via preheating. Furthermore, we analyze the Krylov entropy, which exhibits an evolutionary trend analogous to that of complexity. Crucially, our analysis reveals a dynamical transition in the universe's dissipative nature: with the universe acting as a strongly dissipative system during inflation and transitioning to a weakly dissipative regime in the subsequent eras. These findings provide a novel quantum information perspective on early universe dynamics.