10⁻¹²⁰. That's not just a small number: it's a chasm. That's the ratio of dark energy density to the Planck density, the natural scale of quantum gravity. The colossal difference of 120 orders of magnitude has long seemed an unsolvable puzzle. But the answer might lie in a drama played out at the dawn of time.
The actor of this drama is a Goldstone boson, born from spontaneous breaking of scale symmetry. This symmetry forbids the fundamental theory from having any dimensionful parameters; all scales must arise dynamically. In the earliest moments, when the universe was inflating during the big bang, the action was dictated by R² gravity — an addition to Einstein's theory with the square of spacetime curvature. It hides its own scalar degree of freedom, the scalaron, which together with the symmetry-breaking field, sets the stage. But one character remains frozen.
During inflation, a conserved Noether current fixes the trajectory in field space, and the Goldstone direction is effectively frozen. The metaphor is exact: the field does not evolve; its value sits still, like an actor frozen in the spotlight. Inflation ends, the scene changes, but the actor does not budge — held by the flat direction of the potential. For billions of years he stays in the wings, while the main act, hot matter, dominates the stage. Data from supernovae and the cosmic microwave background confirm: this frozen regime lasted nearly all of history.
Everything changes thanks to unimodular gravity. In this variant of general relativity, the cosmological constant is not a rigid parameter but an integration constant that can evolve. In the late universe, it ‘turns on’ an exponential potential for the Goldstone boson, and a slow, barely perceptible melting begins. The field rolls, and this rolling is detected as dark energy. Its equation-of-state parameter w0 is not exactly −1, but slightly larger: about −0.992. And the melting parameter wa is −0.011. Almost a cosmological constant, but with an elusive drift. Numerical simulations of the field's evolution during the matter era and late acceleration agree perfectly with these numbers.
The model's key insight is a tight formula linking cosmic microwave background inflation parameters to present-day dynamics. The deviation of the inflationary spectral index ns from unity and the tensor-to-scalar ratio r directly determine the melting rate. Simply put: how the actor froze predetermined how he would awaken. For a benchmark, the authors obtain ns ≈ 0.958, r ≈ 0.00287—values consistent with Planck and BICEP/Keck data. Plug them into the relation, and out come w0 and wa. This relation, like a theater program, reveals the director's plan: the squared difference (1 - ns) and the fraction r approximate the square of the normalized melting parameter.
Now the model's fate lies with observers. Telescopes like DESI, Euclid, and the Rubin Observatory will measure the expansion of the universe with unprecedented precision, refining redshifts of distant galaxies. If deviations from a cosmological constant fall within the predicted narrow corridor, it will be a triumph for the idea of scale symmetry. A tiny thaw after an eternal frost, and our sleeping actor finally speaks, revealing a unified script for cosmic history.
The Goldstone boson of scale symmetry remains strictly massless at tree level, but unimodular gravity endows it with a potential of the order of the current dark energy density — about 10⁻¹²⁰ of the Planck density. This is one of the smallest known numbers in physics.
The paper includes an ironic footnote: 'That’s not how the Force works!'—a reference to Han Solo from Star Wars. The authors explain that, despite being massless, the Goldstone boson does not produce a fifth force that could be observed in the laboratory.