Cosmic Attractors and Gauge Hierarchy

TL;DR

The paper tackles the gauge hierarchy problem by treating scalar masses as stochastic quantities that undergo discrete jumps during eternal inflation, driven by brane nucleation. The jump size satisfies $ΔF ∝ φ^{N}$ and $Δφ^{2} ∝ φ^{N}$, yielding a diverging density of states near $φ=0$ with $P_{*}(φ) dφ ∝ dφ/φ^{N}$, i.e., an attractor toward tiny masses. Infrared effects from inflation, notably the Gibbons-Hawking temperature $T_{GH} ∼ H$ and fluctuations $δφ ∼ H$, smear the infinite peak to a small but nonzero scale and tie the post-inflationary Higgs mass to the maximal inflation scale, $H_{max}$. Achieving a TeV-scale Higgs mass requires $H_{max} ∼ 1~{ m TeV}$, and the proposal relies on non-local $F$-form couplings to generate brane charges; it may dovetail with anthropic approaches to the cosmological constant and predicts possible propagating $F$-waves as testable phenomena.

Abstract

We suggest a new cosmological scenario which naturally guarantees the smallness of scalar masses and VEVs, without invoking supersymmetry or any other (non-gravitationaly coupled) new physics at low energies. In our framework, the scalar masses undergo discrete jumps due to nucleation of closed branes during (eternal) inflation. The crucial point is that the step size of variation decreases in the direction of decreasing scalar mass. This scenario yields exponentially large domains with a distribution of scalar masses, which is sharply peaked around a hierarchically small value of the mass. This value is the "attractor point" of the cosmological evolution.