# Optomechanical Analogy for Toy Cosmology with Quantized Scale Factor

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## Abstract

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## 1. Introduction

## 2. The Toy FRW Cosmology

#### 2.1. Simple Examples

#### 2.2. As a Measurement of Scale Factor

#### 2.3. Multiple Measurements

#### 2.4. Classical Dynamics

## 3. Analogy: Optomechanical Cavity

#### 3.1. Cavity as Space

#### 3.2. Cavities as Atoms

#### 3.3. Hubble Expansion in the Rotating Frame

#### 3.4. Logarithmic Scale-Factor

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**The Friedmann–Robertson–Walker–Lemaître (FRW) for an exponentially expanding universe in (

**a**) coordinate and (

**b**) conformal time. Blue vertical lines are separated by one unit of proper distance, while horizontal lines are separated by one unit of proper time. The universe is populated by comoving particles (black disks) which exchange a photon. Color is used to emphasize which frequencies shift.

**Figure 2.**The result of $q(c,a)$ for the simple example with the Lorentzian wavefunctions. Here, ${\gamma}_{0}={\gamma}_{1}={\Gamma}_{0}={\Gamma}_{1}=c=1$, ${\omega}_{0}=10$, and ${\omega}_{1}=5$.

**Figure 3.**A schematic of the coupled two-cavity system. Mirrors to the left of the cavities enable photons to transfer between cavities. The right cavity mirrors share a coupling to a mechanical system (denoted as a spring in the schematic). In addition, the top mirror is driven by a source, while the bottom mirror has an attached detector.

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Smiga, J.A.; Taylor, J.M.
Optomechanical Analogy for Toy Cosmology with Quantized Scale Factor. *Entropy* **2017**, *19*, 485.
https://doi.org/10.3390/e19090485

**AMA Style**

Smiga JA, Taylor JM.
Optomechanical Analogy for Toy Cosmology with Quantized Scale Factor. *Entropy*. 2017; 19(9):485.
https://doi.org/10.3390/e19090485

**Chicago/Turabian Style**

Smiga, Joseph A., and Jacob M. Taylor.
2017. "Optomechanical Analogy for Toy Cosmology with Quantized Scale Factor" *Entropy* 19, no. 9: 485.
https://doi.org/10.3390/e19090485