# Optomechanical analogy for a toy cosmology with a quantized scale factor

## TL;DR

This paper explores a toy cosmological model where quantized electromagnetic fields become entangled with the universe's scale factor, using an optomechanical analogy to simulate quantum back-action effects on cosmological parameters.

## Contribution

It introduces a novel toy model linking quantum electromagnetic fields with the cosmological scale factor and proposes an optomechanical system to experimentally explore these quantum cosmological effects.

## Key findings

- Detection of redshifted photons constrains scale factor superpositions
- Redshift measurement acts as a weak measurement of cosmology
- Optomechanical analogy simulates quantum back-action on the universe's expansion

## Abstract

The simplest cosmology --- the Friedmann-Robertson-Walker-Lema\^{i}tre (FRW) model --- describes a spatially homogeneous and isotropic universe where the scale factor is the only dynamical parameter. Here we consider how quantized electromagnetic fields become entangled with the scale factor in a toy version of the FRW model. A system consisting of a photon, source, and detector is described in such a universe, and we find that the detection of a redshifted photon by the detector system constrains possible scale factor superpositions. Thus, measuring the redshift of the photon is equivalent to a weak measurement of the underlying cosmology. We also consider a potential optomechanical analogy system that would enable experimental exploration of these concepts. The analogy focuses on the effects of photon redshift measurement as a quantum back-action on metric variables, where the position of a movable mirror plays the role of the scale factor. By working in the rotating frame, an effective Hubble equation can be simulated with a simple free moving mirror.