Planck scale from broken local conformal invariance in Weyl geometry
Abstract
We show that in a quadratic gravity based on Weyl's conformal geometry, the Planck mass scale can be generated from quantum effects of the gravitational field and the Weyl gauge field via the Coleman-Weinberg mechanism where a local scale symmetry is broken. At the same time, the Weyl gauge field acquires a mass less than the Planck mass by absorbing the scalar graviton. The shape of the effective potential is almost flat owing to a gravitational character and high symmetries, so our model would provide for an attractive model for the inflationary universe. We also present a toy model showing spontaneous symmetry breakdown of a global scale symmetry by moving from the Jordan frame to the Einstein one, and point out its problems.
Keywords
Cite
@article{arxiv.2003.12256,
title = {Planck scale from broken local conformal invariance in Weyl geometry},
author = {Ichiro Oda},
journal= {arXiv preprint arXiv:2003.12256},
year = {2020}
}
Comments
17 pages; Contribution to the Proceedings of the Corfu Summer Institute 2019, 31 Aug - 25 Sep 2019, Corfu, Greece. arXiv admin note: substantial text overlap with arXiv:1903.09309