Abstract
The simplest cosmology—the Friedmann–Robertson–Walker–Lemaître (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.
Highlights
Quantum mechanics provides several key mechanisms for proposed explanations of cosmological structure [1]
A toy FRW quantum cosmology was proposed in which a metric variable was treated as a quantum variable
The scale factor in the tFRW model was promoted to the quantum operator â, and a metric wavefunction was defined as a superposition of scale factor eigenstates
Summary
Quantum mechanics provides several key mechanisms for proposed explanations of cosmological structure [1]. We consider a toy cosmology based upon the Friedmann–Robertson–Walker–Lemaître (FRW) model, where the scale factor is quantized, and a wavefunction describing the state of the metric is defined. This wavefunction is often explored in the context of its dynamics as constrained by the Wheeler–DeWitt equation [10,11,12,13,14]. The motion of a mirror in an optical cavity induces a redshift in cavity photons This process leads to entanglement between an effective scale factor and the sources and detectors that emulates cosmological redshift. We can envision testing quantum cosmology concepts in this toy model setting
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