How large is our Universe?

New study shows we may already be observing a significant fraction of the Universe.

September 12, 2023

Many cosmological models assume that the Universe is very large, it may even be infinite. In a new paper two researchers from the ERC research group Theoretical Cosmology at AEI Potsdam and the University of Waterloo present a model in which the Universe is comparably small: not much larger than what we can currently observe. The researchers built their model on the Hartle–Hawking no-boundary proposal, in which the Universe comes into existence from nothing via a tunnelling event. This quantum event can be described by a spacetime in which time and space are allowed to take complex values. However, not all such complex spacetimes make sense mathematically and may develop instabilities. The researchers show that for inflationary potentials compatible with observations of the early Universe, the restriction to allowable spacetimes implies that inflation must have lasted longer than a certain minimal amount. They find that this is precisely the amount needed to expand the Universe to its current size. Moreover, the no-boundary proposal assigns the highest probability to those cosmic histories with minimal inflation. Thus, in this model, it is likely that we are already seeing a significant fraction of the entire Universe.

Paper abstract

A plot of the predictions of the natural inflation models considered here with various parameter values f and compared to the observational bounds obtained by the Planck satellite (in green) and the BICEP/Keck experiments (in blue). The colour coding depicts the number of e-folds from the time of horizon exit until the end of inflation.

A plot of the predictions of the natural inflation models considered here with various parameter values f and compared to the observational bounds obtained by the Planck satellite (in green) and the BICEP/Keck experiments (in blue). The colour coding depicts the number of e-folds from the time of horizon exit until the end of inflation.

Many cosmological models assume or imply that the total size of the universe is very large, perhaps even infinite. Here we argue instead that the universe might be comparatively small, in fact not much larger than the currently observed size. A concrete implementation of this idea is provided by the no-boundary proposal, in combination with a plateau-shaped inflationary potential. In this model, opposing effects of the weighting of the wave function and of the criterion of allowability of the geometries conspire to favour small universes. We point out that a small size of the universe also fits well with swampland conjectures, and we comment on the relation with the dark dimension scenario.