We present a new solution to the hierarchy problem, where the Higgs boson mass is at its observed electroweak value because such a patch inflates the most in the early Universe. If the Higgs boson mass depends on a field undergoing quantum fluctuations during inflation, then inflation will fill the Universe with the Higgs boson mass that corresponds to the largest vacuum energy. The hierarchy problem is solved if the maximum vacuum energy occurs for the observed Higgs boson mass. We demonstrate this notion with a proof-of-principle model containing an axion, a modulus field and the Higgs boson, and show that inflation can be responsible for the weak scale.
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We are grateful to Anson Hook, Liam McAllister, Hitoshi Murayama, Gilad Perez, and Raman Sundrum for discussions and comments on the manuscript. The work of Y. H. is supported by the Israel Science Foundation (Grant No. 1112/17), by the Binational Science Foundation (Grant No. 2016155), by the I-CORE Program of the Planning Budgeting Committee (Grant No. 1937/12), by the German Israel Foundation (Grant No. I-2487-303.7/2017), and by the Azrieli Foundation. E. K. is supported by the Israel Science Foundation (Grant No. 1111/17), by the Binational Science Foundation (Grant No. 2016153), and by the I-CORE Program of the Planning Budgeting Committee (Grant No. 1937/12). M. G. was supported in part by the NSF under Grant No. PHY-1620074 and by the Maryland Center for Fundamental Physics (MCFP). Y. H. and E. K. would like to express a special thanks to the Mainz Institute for Theoretical Physics (MITP) in Capri for its hospitality and support. The work of M. G. was in part performed at the Aspen Center for Physics, which is supported by National Science Foundation Grant No. PHY-1607611.
© 2019 authors.