It does seem interesting! I hope it's OK to unpack some of the references. Show the abstract and the Natalie Wolchover link
https://www.quantamagazine.org/20150527-a-new-theory-to-explain-the-higgs-mass/
==excerpts==
Their solution traces the hierarchy between gravity and the other fundamental forces back to the explosive birth of the cosmos, when, their model suggests, two variables that were evolving in tandem suddenly deadlocked. At that instant, a hypothetical particle called the “axion” locked the Higgs boson into its present-day mass, far below the scale of gravity...
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Since the 1980s, the most popular proposal has been supersymmetry. It solves the hierarchy problem by postulating a yet-to-be-discovered twin for each elementary particle... Twins contribute opposite terms to the mass of the Higgs boson, rendering it immune to the effects of super-heavy gravity particles (since they are nullified by the effects of their twins).
But
no evidence for supersymmetry or for any competing ideas — such as “technicolor” and “warped extra dimensions” — turned up during the first run of the LHC from 2010 to 2013. When the collider shut down for upgrades in early 2013 without having found a single “sparticle” or any other sign of physics beyond the Standard Model, many experts felt they could no longer avoid contemplating a stark alternative. What if the Higgs mass, and by implication the laws of nature, are unnatural?
...
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In their model, the Higgs mass depends on the numerical value of a hypothetical field that permeates space and time: an axion field. To picture it, “we think of the totality of space as being this 3-D mattress,” Dimopoulos said. The value at each point in the field corresponds to how compressed the mattress springs are there. It has long been recognized that the existence of this mattress — and its vibrations in the form of axions — could solve two deep mysteries: First, the axion field would explain why most interactions between protons and neutrons run both forward and backward,
solving what’s known as the “strong CP” problem. And axions could make up dark matter. Solving the hierarchy problem would be a third impressive achievement.
The story of the new model begins when the cosmos was an energy-infused dot. The axion mattress was extremely compressed, which made the Higgs mass enormous. As the universe expanded, the springs relaxed, as if their energy were spreading through the springs of the newly created space. As the energy dissipated, so did the Higgs mass. When the mass fell to its present value, it caused a related variable to plunge past zero, switching on the Higgs field, a molasseslike entity that gives mass to the particles that move through it, such as electrons and quarks. Massive quarks in turn interacted with the axion field, creating ridges in the metaphoric hill that its energy had been rolling down. The axion field got stuck. And so did the Higgs mass...
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==endquote==
http://arxiv.org/abs/1504.07551
Cosmological Relaxation of the Electroweak Scale
Peter W. Graham,
David E. Kaplan,
Surjeet Rajendran
(Submitted on 28 Apr 2015 (
v1), last revised 22 Jun 2015 (this version, v2))
A new class of solutions to the electroweak hierarchy problem is presented that does not require either weak scale dynamics or anthropics. Dynamical evolution during the early universe drives the Higgs mass to a value much smaller than the cutoff. The simplest model has the particle content of the standard model plus a QCD axion and an inflation sector. The highest cutoff achieved in any technically natural model is 10^8 GeV.
Comments: 10 pages, 2 figures. v2: We describe a way in which the bound on the cutoff in the QCD model can be raised to 1000 TeV. We've added a discussion of constraints on reheating. An additional constraint is noted for the non-QCD model. Other clarifications of the model added throughout