Optimal estimation of parameters for scalar fields in expanding universe exhibiting Lorentz invariance violation

TL;DR

This paper explores how Lorentz invariance violation (LIV) influences the optimal quantum estimation of parameters in a scalar field within an expanding universe, showing that LIV can enhance measurement precision under certain conditions.

Contribution

It introduces a framework for optimal quantum parameter estimation in LIV-affected scalar fields in expanding spacetimes, highlighting conditions for improved precision.

Findings

LIV can improve bounds on cosmological parameter estimation.

Optimal precision is achieved with suitable LIV, cosmological, and field parameters.

Projective measurements onto specific probe states enhance parameter estimation accuracy.

Abstract

We address the optimal estimation of quantum parameters, in the framework of local quantum estimation theory, for a massive scalar quantum field in the expanding Robertson-Walker universe exhibiting Lorentz invariance violation (LIV). The information about the history of the expanding spacetime in the presence of LIV can be extracted by taking measurements on the entangled state of particle modes. We find that, in the estimation of cosmological parameters, the ultimate bounds to the precision of the Lorentz-invariant massive scalar field can be improved due to the effects of LIV under some appropriate conditions. We also show that, in the Lorentz-invariant massive scalar field and massless scalar field due to LIV backgrounds, the optimal precision can be achieved by choosing the particles with some suitable LIV, cosmological and field parameters. Moreover, in the estimation of LIV parameter during the spacetime expansion, we prove that the appropriate momentum mode of field particles and larger cosmological parameters can provide us a better precision. Particularly, the optimal precision of the parameters estimation can be obtained by performing projective measurements implemented by the projectors onto the eigenvectors of specific probe states.