Cosmology from Quantum Information

Abstract

We describe inflation in terms of a time dependent quantum density matrix with time playing the role of a stochastic variable. Using a quasi-de Sitter model we compute the corresponding quantum Fisher information function as the second derivative of the relative entanglement entropy for the density matrix at two different times. Employing standard quantum estimation theory we evaluate the minimal variance of quantum scalar fluctuations that reproduces the power spectrum and the corresponding tilt in the slow roll limit. The Jeffreys prior associated with such Fisher information can be used to define the probabilities on the set of initial conditions defined by the slow roll parameter $\epsilon$ and the initial Shannon information.

arXiv commentextended discussion in general and in particular for fluctuation curvature power spectrum and citations added

References in corpus (5)

• The Role of Relative Entropy in Quantum Information Theory
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Inflation
• A Measure of de Sitter Entropy and Eternal Inflation
• Cosmological Complexity
• Complexity and Time

Cited by in corpus (11)

• Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies
• Cosmic decoherence: primordial power spectra and non-Gaussianities
• The Early Universe as an Open Quantum System: Complexity and Decoherence
• Model Independent Prediction of the Spectral Index of Primordial Quantum Fluctuations
• Dynamically Generated Inflationary Lambda-CDM
• Dark matter from primordial quantum information
• Quantum Fisher Cosmology: Confronting Observations and the Trans-Planckian Problem
• The Quantum Origin of Quasi de Sitter: a Model Independent Quantum Cosmological Tilt
• The quantum cosmological tilt and the origin of dark matter
• Topological susceptibility and information theory
• The quantum de Sitter root of quasi de Sitter observables: a pedagogical review