Abstract
We compute the quantum circuit complexity of the evolution of scalar curvature perturbations on expanding backgrounds, using the language of squeezed vacuum states. In particular, we construct a simple cosmological model consisting of an early-time period of de Sitter expansion followed by a radiation-dominated era and track the evolution of complexity throughout this history. During early-time de Sitter expansion the complexity grows linearly with the number of e-folds for modes outside the horizon. The evolution of complexity also suggests that the Universe behaves like a chaotic system during this era, for which we propose a scrambling time and Lyapunov exponent. During the radiation-dominated era, however, the complexity decreases until it "freezes in" after horizon re-entry, leading to a "de-complexification" of the Universe.
Highlights
In recent years, quantum information theory has played the role of a melting pot for various branches of physics
Quantum information theory is helping to shape our understanding about fundamental properties of nature, and quantum complexity plays a major role
In this paper we have applied Nielsen’s geometric approach to compute the complexity of the Universe; we computed the complexity of scalar cosmological perturbations by taking our reference state as the unsqueezed ground state and our target state as the squeezed vacuum state representing the evolution of cosmological perturbations
Summary
Quantum information theory has played the role of a melting pot for various branches of physics. It is conjectured that these two objects are dual to the so-called “complexity” of the dual field theory state For this reason these proposals are known as the CV (complexity 1⁄4 volume) [5] and CA (complexity 1⁄4 action) [7] conjectures, respectively. Quantum complexity may be a possible diagnostic for quantum chaos, and is considered as an integral part of the web of diagnostics for quantum chaos [29,30,31,32,33,34,35] It was highlighted in [32] that circuit complexity can provide essential information (such as the scrambling time, Lyapunov exponent, etc.) about a quantum chaotic system. We will choose the ground state while the mode is inside the horizon as our reference state, and study complexity for a target state consisting of the time-evolved cosmological perturbation on the expanding background.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
