How the Universe is Born from Nothing express
Quantum nothingness resembles water in a pot just before boiling. From time to time, a bubble spontaneously swells up — but not of steam, but of an entire universe. Such a bubble doesn't collapse; instead, it inflates into spacetime, triggering its own Big Bang. The only question is how often this happens.
Physicists took this metaphor seriously and calculated the exact probability. They used a mathematical trick: treating time as a fourth spatial dimension. The resulting formula resembles the one describing a particle passing through a wall. Previously, only the main factor was considered, which made the chance vanishingly small. Now they added quantum fluctuations — chaotic jitters inherent to every bubble at the quantum level. These turn a rough estimate into a precise calculation.
Ultimately, they obtained a simple formula where the chance of a Universe appearing from nothing is expressed through familiar physical constants. Most surprising: structurally, it barely differs from calculations for elementary particles — as if the entire cosmos behaves like one big quantum object.
Original abstract
as written by the authors arXiv:2605.16150
We consider the quantum creation of a closed universe within the Euclidean path-integral formalism. An analytical expression for the tunneling probability is derived, including both the exponential suppression and the exact Gaussian prefactor due to quadratic fluctuations around the instanton. The calculation is performed in a fixed-interval minisuperspace formulation, where the Hamiltonian constraint is imposed at the level of the classical instanton, while the full lapse integration is not included beyond the leading semiclassical approximation. The result provides a transparent and self-consistent semiclassical estimate of the nucleation rate, refining previous analyses with the inclusion of Gaussian fluctuations.
In quantum physics, even a particle can pass through a wall. It turns out that mathematically, a whole universe is no different — it's the largest 'tunneling' object ever studied by scientists.