Historical research guide · 0762 · 2021
Yoga Dark Energy: Natural Relaxation and Other Dark Implications of a Supersymmetric Gravity Sector
C. P. Burgess · Danielle Dineen · F. Quevedo
In one minute
Cliff Burgess, Danielle Dineen and Fernando Quevedo take on the oldest embarrassment in physics: the vacuum of quantum field theory should weigh enormously, and the universe behaves as though it weighs almost nothing. Their answer is a ‘yoga’ model — naturally relaxed — that combines three ingredients none of which works alone. Gravity stays supersymmetric down to very low energies; a new light scalar they call the relaxon slides until it cancels the largest term; and an approximate scale symmetry, carried by a field called the dilaton, wipes out the next term as well. What survives is small, positive, and the right size for the dark energy we actually measure. The same dilaton then fixes the weak scale, which explains why it sits near the geometric mean of the Planck and dark-energy scales. The price is a very light dilaton, still cosmologically active today — so this model predicts dark energy that evolves, particle masses that drift, and a fifth force hidden by its axion partner.
Connection
Chapters 2 and 13 turn on the question of what the vacuum energy actually is and why the number we measure is so far from the number the field theory hands us. This paper is one of the most careful attempts to make the small value natural rather than accidental, and it does so by giving the vacuum structure — a dilaton and an axion that are still moving today. That makes dark energy something with dynamics you can look for, which is exactly the site’s reading of it in chapter 3. Read it beside the supernova reconstruction method at /library/stm-a5aa9f6416 and the DESI DR2 measurement at /library/stm-15541611e8, which is where the evolving equation of state this model predicts would first show up.
From the source
Three ingredients, none of which suffices on its own, together suppress the gravitational response of heavy-particle vacuum energies: a very supersymmetric gravity sector coupled to a Standard Model in which supersymmetry is non-linearly realised, a relaxation mechanism driven by a light scalar the authors call the relaxon, and an accidental approximate scale invariance carried by a low-energy dilaton supermultiplet. All three are common in higher-dimensional and string constructions.Abstract; Section 1, Introduction, items (i) to (iii)
The dilaton’s expectation value τ sets the weak scale, which comes out as the Planck mass divided by the square root of τ. A minor tuning of lagrangian parameters of order one part in sixty stabilises τ at about 10 to the 26th, because the relevant part of the scalar potential is a rational function of the logarithm of τ rather than of τ itself, so an astronomically large minimum needs only modest input numbers.Abstract; Section 6, opening summary
The low-energy potential is a series in 1/τ. The relaxon zeroes the leading term, and the interplay of scale invariance and supersymmetry — extended no-scale structure — makes the next term vanish as well, leaving a naturally small positive cosmological constant of order the fourth power of the ratio of the TeV scale squared to the Planck mass, which is the observed size. This also reproduces the old observation that the weak scale is the geometric mean of the Planck and cosmological-constant scales.Section 6, Equation 6.1 and the paragraphs following it
Any successful suppression of the cosmological constant in this framework forces the dilaton to be very light, with a mass of order the present-day Hubble scale, and therefore still cosmologically active. Dark energy is then not a constant at all but a specific near-scale-invariant quintessence, and — remarkably, in the authors’ word — both the vacuum energy and the quintessence mass are technically natural.Section 1, Introduction; Section 5.1, Dilaton dark energy
Scale invariance forces the dilaton to couple to ordinary matter like a Brans-Dicke scalar, with a strength that solar-system tests of gravity would naively already have ruled out. The escape is that the dilaton arrives paired with an axion, and the axion-dilaton self-couplings divert matter-dilaton couplings into generating axion fields instead, which barely move test particles. The authors name the mechanism ‘axion homeopathy’, because it works even for extremely small direct axion-matter couplings, provided they are not exactly zero.Section 1, Introduction; Section 4.2, Axio-dilaton couplings and tests of gravity
The authors name their own bills. A τ of at least 10 to the 26th drives the axion decay constant down to about 10 eV, so the four-dimensional effective theory must fail at eV energies and needs a completion — supersymmetric large extra dimensions are the candidate, and the simplest string models would cap τ near 10 to the 20th instead. What to watch: whether extra dimensions supply that completion, whether the predicted drift of particle masses over cosmic time survives observation, and whether that same drift resolves the Hubble tension.Section 6, ‘There are several prices we pay’; Section 6.2, future directions
The way in
https://arxiv.org/abs/2111.07286How to cite it
C. P. Burgess, Danielle Dineen, F. Quevedo (2021) Yoga Dark Energy: Natural Relaxation and Other Dark Implications of a Supersymmetric Gravity Sector arXiv:2111.07286