## Abstract

I consider a quantum system that possesses key features of quantum shape dynamics and show that the evolution of wave-packets will become increasingly classical at late times and tend to evolve more and more like an expanding classical system. At early times however, semiclassical effects become large and lead to an exponential mismatch of the apparent scale as compared to the expected classical evolution of the scale degree of freedom. This quantum inflation of an emergent and effectively classical system, occurs naturally in the quantum shape dynamics description of the system, while it is unclear whether and how it might arise in a constrained Hamiltonian quantization.

## Keywords

Shape dynamics Quantum effect Inflation Bohmian trajectory## Notes

### Acknowledgements

This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC) through a grant to the University of New Brunswick and by the Foundational Questions Institute through Grant FQXi-RFP3-1339. I am very grateful for an invitation to the 2013 “Haunted Workshop” in Tepoztlan, Mexico, where discussions with Ward Struyve and Daniel Sudarsky raised the question about quantum corrections to classical shape dynamics cosmology was raised. It was also at this workshop where Ward Struyve introduced me to detail about Bohmian mechanics.

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