Is the universe infinite?

Curvature would distort the apparent size of features in the oldest light. Measured against the physical size those features should have, the microwave background gives a curvature consistent with zero to within a fraction of a per cent when combined with galaxy surveys.

Flat is not the same as infinite. That a flat universe extends forever is the usual hypothesis, and the Particle Data Group's review of the field says observations cannot tell whether it is true.

If space closes on itself on a scale smaller than the observable region, light could cross it more than once, and the same patch of early universe would appear in two directions. The matching patterns would show up as correlated circles in the microwave sky.

That search was carried out systematically on the Planck maps. Nothing was found, which puts a lower bound on the size of a repeating cell for the shapes tested. For the shapes that would print matching circles in opposite directions, the bound is close to the distance to the last scattering surface. The loosest shape tested, a slab, is held only to about half of it. Later work showed that the bound is not the same for every shape: in all but the simplest, the shortest loop around the universe can miss us and be two to six or more times shorter than the diameter of that surface.

In 2019 Di Valentino, Melchiorri and Silk argued that the Planck power spectra on their own prefer a closed universe at better than 99 per cent confidence, and that assuming the universe is flat could mask a crisis in cosmology. The argument turns on a subtle feature of how the microwave background is gravitationally lensed.

Most of the field reads the combined data as flat, and a reanalysis of the same maps by Efstathiou and Gratton traces the preference for curvature to which likelihood was used and to the prior placed on curvature itself. The disagreement is about which combinations are legitimate, which is a real methodological question and not a rhetorical one. The DESI galaxy survey's 2025 results, combined with the microwave background, find no significant preference for curvature either.

Everything above constrains the universe out to about the horizon. Beyond that, nothing can be observed now, because no signal has had time to arrive, and the acceleration means that from far enough away none ever will.

Statements about the extent of the whole are therefore extrapolations of uniformity: the assumption that what cannot be seen resembles what can. That assumption is reasonable and it is not evidence.

If inflation happened and does not stop everywhere, it produces regions that stop inflating at different times, separated by space still expanding too fast for anything to cross. Each would look, from inside, like a universe.

This is a consequence of models built for other reasons rather than a proposal made for its own sake, which is the strongest thing that can be said for it. It also has no accepted observational test, which is the strongest thing that can be said against it.