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

Optomechanical analogy for a toy cosmology with a quantized scale factor