Is the universe infinite or do we say that because we have not travelled to or seen its walls yet? originally appeared on Quora, the place to gain and share knowledge, empowering people to learn from others and better understand the world. You can follow Quora on Twitter, Facebook, and Google Plus.
The simplest cosmology that fits the large-scale characteristics of the universe is the so-called Friedmann—Lemaître—Robertson—Walker cosmology describing a spacetime that is homogeneous (same everywhere) and isotropic (has no preferred direction).
This simple cosmology is characterized, among other things, by a variable that represents spatial curvature. It can be positive, negative, or zero.
Our best observations to date strongly suggest that the universe has no spatial curvature. It may be expanding in time, but the geometry of space, at any given time, is Euclidean.
The simplest topology that corresponds to Euclidean geometry is that of flat, infinite space. So by Occam’s razor, i.e., the parsimony of assumptions, we can conclude that in the absence of evidence to the contrary, the universe appears infinite.
That does not mean that we know this for sure. In fact, there really is no way of knowing. What is beyond the limits of the observable universe is, well, not observable, not even in principle. So for all we know, just outside the observable universe there is a big bad wall. Or a brane-type singularity. Or fire-breathing pink unicorns preventing us from going any further. Nature is under no obligation, after all, to behave in a manner that we humans call reasonable.
But in our experience, Nature by and large does behave reasonably, and we might expect it to continue behaving reasonably even beyond the boundaries of the observable universe. That expectation, combined with the observation that the universe appears to lack spatial curvature, leads to the concept of a spatially infinite universe.
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