Inflating to the Weak Scale

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.

Figure 1

The axion potential. Top: The axion is initially misaligned from the global minimum and is trapped at a local minimum of the potential. Bottom: As $\varphi$ increases and the Higgs boson VEV drops, the QCD-induced part of the potential releases its barriers and the axion is free to roll down to the global minimum.

Figure 2

Total contributions to the vacuum energy. The green dashed curve shows the axion potential energy at the end of inflation, the dashed orange curve depicts the $\varphi$ potential, and the total contributions are shown in solid blue.