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.

• Received 19 February 2020
• Accepted 27 August 2020

DOI:https://doi.org/10.1103/PhysRevD.102.063511

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society