Cosmological selection of a small weak scale from large vacuum energy: a minimal approach

TL;DR

This paper proposes a minimal cosmological model with a landscape of vacua to explain the small electroweak scale, linking vacuum energy peaks during inflation to the hierarchy problem, and predicts testable Higgs and dark matter properties.

Contribution

It introduces a simple landscape-based mechanism involving a pseudoscalar and extra Higgs doublet to naturally select a small electroweak scale without complex new physics.

Findings

Vacuum energy peaks at small electroweak VEVs during inflation.

Predicts specific relationships between Higgs boson masses and couplings.

Pseudoscalar can account for dark matter relic density.

Abstract

We present a minimal cosmological solution to the hierarchy problem. Our model consists of a light pseudoscalar and an extra Higgs doublet in addition to the field content of the Standard Model. We consider a landscape of vacua with varying values of the electroweak vacuum expectation value (VEV). The vacuum energy in our model peaks in a region of the landscape where the electroweak VEV is non-zero and much smaller than the cutoff. During inflation, due to exponential expansion, such regions of the landscape with maximal vacuum energy, dominate the universe in volume, thus explaining the smallness of the electroweak scale with respect to the cutoff. The pseudoscalar potential in our model is that of a completely generic pseudogoldstone boson$-$not requiring the clockwork mechanism$-$and its field value never exceeds its decay constant or the Planck scale. Our mechanism is robust to the variation of other model parameters in the landscape along with the electroweak VEV. It also predicts a precise and falsifiable relationship between the masses and couplings of the different Higgs boson mass-eigenstates. Moreover, the pseudoscalar in our model can account for the observed dark matter relic density.