Simple

The Donut Universe: How a Simple Shape Explained the Birth of the Cosmos

Original: "Inflation and topology from the no-boundary state"
· Victor Godet
arXiv:2605.05317v2 · 2026-05-06 · CC BY · ⏱ 1 min · HEP Theory General Relativity
A three-dimensional donut turns the quantum birth of the world into a simple and almost inevitable scenario with long inflation.
Abstract

Quantum physics predicts that our universe could have been born tiny — and stayed that way. But observations say it's enormous. It turns out that if you imagine space not as a sphere, but as a doughnut (a torus), the math gives birth to a big world with a long expansion. So, maybe we live in a cosmic doughnut?

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The Universe could have been born from 'nothing' during the quantum Big Bang, like a soap bubble — suggested Hawking. But calculations yielded a tiny world that would instantly collapse into a point.

The way out was found by geometry. Replace the familiar sphere with a three-dimensional donut. Thanks to its hole, the donut offers many ways to loop around: you can thread a loop through the hole, or wrap around the outside. Each such loop represents a distinct quantum birth path. When physicists summed up these possibilities, long inflation — superfast expansion — turned from a rarity into a near inevitability. Thus, Guth's idea gained firm support.

Unexpectedly, in the calculations, the Riemann zeta function emerged — a mysterious staircase into the world of prime numbers. It turned out that a donut-universe almost certainly inflates by a factor of 10^108. Gravity and spacetime curvature don't distort the overall picture, and ancient light (cosmic microwave background) carries the echo of that birth.

🎯 In the calculations, the Riemann zeta function unexpectedly popped up — a mysterious mathematical construct linking the distribution of prime numbers to the fabric of the Universe.

\langle \Psi | \Psi \rangle \propto \frac{M_P^4}{V(\phi_*)}
The norm of the Hartle-Hawking wave function for T³—the probability of starting inflation is inversely proportional to the potential, not exponentially small.
P(N) = 2\varepsilon_V e^{-2\varepsilon_V N}
Exponential distribution of the number of e-folds with a mean N ≈ 1/(2ε_V) ≈ 250.
Scientists
Alan GuthAndrei LindeGeorges LemaîtreJames PeeblesAdam RiessBrian Schmidt
Tags
big bang expansion of the universe cosmic microwave background spacetime curvature gravity Quantum Field numerical simulation inflation
Laws
Friedmann equationsHubble's lawNoether's theoremEinstein field equationsPlanck's lawequivalence principle
Original: arXiv:2605.05317v2 · CC BY · bridge42worlds