A simple application of quantum metrology to isotropic and anisotropic spacetimes

In this work, we study quantum metrology protocol in the context of relativistic quantum fields in curved spacetimes. In particular, we restrict our attention to the isotropic and anisotropic models. We investigate how the oscillatory anisotropy affects a quantum metrology protocol. Here, the oscillatory anisotropy is incorporated as a small gravitational disturbance. We calculate the Fisher information for both cosmological parameters Formula: see text (expansion volume) and Formula: see text (expansion rate). We find that, unlike the isotropic case, the Fisher information of both the parameters Formula: see text and Formula: see text are oscillating functions of the momentum Formula: see text. The oscillatory spectra of Fisher information can theoretically be understood as results of the dependence of the Bogoliubov coefficients on the anisotropic oscillations. In principle, this framework can be used to infer about the underlying spacetime structure and examine the effects of the universe scale factor oscillations.