Inflationary Krylov complexity

Abstract

In this work, we have systematically investigated the Krylov complexity of curvature perturbation for the modified dispersion relation in inflation, using the algorithm in closed system and open system. Our analysis could be applied to the most inflationary models. Following the Lanczos algorithm, we find the very early universe is an infinite, many-body, and maximal chaotic system. Our numerics shows that the Lanczos coefficient and Lyapunov index of the standard dispersion relation are mainly determined by the scale factor. As for the modified case, it is nearly determined by the momentum. In a method of the closed system, we discover that the Krylov complexity will show irregular oscillation before the horizon exits. The modified case will present faster growth after the horizon exists. Since the whole universe is an open system, the approach of an open system is more realistic and reliable. Then, we construct the exact wave function which is very robust only requiring the Lanczos coefficient proportional to $n$ (main quantum number). Based on it, we find the Krylov complexity and Krylov entropy could nicely recover in the case of a closed system under the weak dissipative approximation, in which our analysis shows that the evolution of Krylov complexity will not be the same with the original situation. We also find the inflationary period is a strong dissipative system. Meanwhile, our numerics clearly shows the Krylov complexity will grow during the whole inflationary period. But for the small scales, there will be a peak after the horizon exits. Our analysis reveals that the dramatic change in background (inflation) will significantly impact the evolution of Krylov complexity. Since the curvature perturbation will transit from the quantum level to the classical level.

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References in corpus (15)

• The Effective Field Theory of Inflation
• Complexity and Shock Wave Geometries
• Quantum Computation as Geometry
• Horava-Lifshitz Cosmology
• Cosmology of the Lifshitz universe
• Non-singular cosmology in a model of non-relativistic gravity
• Krylov Localization and suppression of complexity
• A String-Inspired Quintom Model Of Dark Energy
• Primordial perturbation with a modified dispersion relation
• Operator dynamics in Lindbladian SYK: a Krylov complexity perspective
• Emergent Universe Scenario via Quintom Matter
• Spectral and Krylov Complexity in Billiard Systems
• Near Scale Invariance with Modified Dispersion Relations
• $CPT$ Violating Electrodynamics and Chern-Simons Modified Gravity
• Krylov Complexity in Lifshitz-type Scalar Field Theories

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• Brickwall One-Loop Determinant: Spectral Statistics & Krylov Complexity
• Krylov Complexity in the Schrödinger Field Theory
• Inflationary power spectrum from the Lanczos algorithm
• Probing Krylov Complexity in Scalar Field Theory with General Temperatures
• Does relativistic motion really freeze initially maximal entanglement?
• Krylov complexity of purification
• Detecting quantum chaos via pseudo-entropy
• Krylov complexity of thermal state in early universe
• Bosonic and fermionic mutual information of N-partite systems in dilaton black hole background
• Krylov complexity and Wightman power spectrum with positive chemical potential in Schrödinger field theory
• Non-monotonic evolution of multipartite entanglement under the Unruh effect
• Generalized CV Conjecture and Krylov Complexity in Two-Mode Hermitian Systems via Information Geometry