Quantum estimation of cosmological parameters

TL;DR

This paper applies quantum metrology to cosmological perturbations to determine the ultimate precision limits in estimating primordial parameters, revealing significant gaps between classical and quantum information in inflationary models.

Contribution

It introduces the use of quantum Fisher information to cosmological perturbations, quantifies the quantum limits of parameter estimation, and compares them to classical measurements.

Findings

Quantum Fisher information exceeds classical bounds exponentially with e-folds outside the horizon.

Accessing the decaying mode is necessary for exponential improvements in tensor-to-scalar ratio estimation.

There exists a highly efficient but currently inaccessible optimal measurement.

Abstract

Understanding how well future cosmological experiments can reconstruct the mechanism that generated primordial inhomogeneities is key to assessing the extent to which cosmology can inform fundamental physics. In this work, we apply a quantum metrology tool - the quantum Fisher information - to the squeezed quantum state describing cosmological perturbations at the end of inflation. This quantifies the ultimate precision achievable in parameter estimation, assuming ideal access to early-universe information. By comparing the quantum Fisher information to its classical counterpart - derived from measurements of the curvature perturbation power spectrum alone (homodyne measurement) - we evaluate how close current observations come to this quantum limit. Focusing on the tensor-to-scalar ratio as a case study, we find that the gap between classical and quantum Fisher information grows exponentially with the number of e-folds a mode spends outside the horizon. This suggests the existence of a highly efficient (but presently inaccessible) optimal measurement. Conversely, we show that accessing the decaying mode of inflationary perturbations is a necessary (but not sufficient) condition for exponentially improving the inference of the tensor-to-scalar ratio.