Simple

The Waffle Explanation for the Dark Energy Mystery

Original: "Small Vacuum Energy and Tunneling in a Modified Bousso-Polchinski Model"
arXiv:2605.05357v1 · 2026-05-06 · CC BY 4.0 · ⏱ 1 min · HEP Theory Cosmology General Relativity
Comparing vacua to a waffle structure showed that the smallness of dark energy is almost inevitable.
Abstract

Imagine: the density of dark energy in the Universe is like the thickness of the thinnest pancake in a stack. Scientists studied possible worlds from string theory and found that in 99.95% of them, the energy density turns out to be exactly as tiny as we observe. Why are we so lucky?

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After the Big Bang, the Universe not only expands—its expansion is accelerated by mysterious dark energy, discovered by Adam Riess. The trouble is that calculations from particle physics predict an energy 10¹²⁰ times greater than what we observe—the greatest blunder in science.

The answer lies in string theory: all particles are tiny vibrating strings, and hidden dimensions are curled up into microscopic knots. The shape of this knot determines the properties of the world, and the number of possible shapes is astronomical. Leonard Susskind compared them to a dense waffle lattice. Among a myriad of cells, it’s almost inevitable to find one with a tiny dimple—a vacuum with low energy. Simulations based on 532 million geometries showed: in 99.95% of cases, the lattice spacing is so fine that a value close to zero arises naturally, without fine-tuning.

But the biggest surprise is the scale: the number of possible vacua is estimated at 10²⁷²⁰⁰⁰, exceeding the number of atoms in the entire visible Universe. Transitions between them are not smooth but giant leaps, linking the early inflationary stage (hypothesis of Alan Guth) and even the Standard Model of particles with the microscopic properties of space.

🎯 In one of the geometries, the number of vacua is estimated at 10²⁷²⁰⁰⁰—a one with 272 thousand zeros, immeasurably larger than the number of atoms in the visible Universe.

V = \Lambda_{0} - \frac{3}{\mathcal{V}^{2}} \left| N^{I} \Pi_{I} \right|^{2}
Vacuum energy as the difference of a positive uplift and the contribution from twisted fluxes.
\frac{24 J}{e \pi \chi} > 1
Constraint on Hodge numbers ensuring metastability of the Universe.
Scientists
Alan GuthAndrei LindeGeorges LemaîtreJames PeeblesAdam RiessBrian Schmidt
Tags
dark energy string theory inflation big bang expansion of the universe Standard Model Quantum Field numerical simulation
Laws
Friedmann equationsHubble's lawNoether's theoremEinstein field equationsPlanck's lawspin–statistics theorem
Original: arXiv:2605.05357v1 · CC BY 4.0 · bridge42worlds