A Small Universe Case

The universe is vast, as Douglas Adams would say.

The most distant light we can see is the cosmic microwave background (CMB), which took more than 13 billion years to reach us.

This marks the limit of the visible universe, and while you might think that means the Universe is 26 billion light years across, due to cosmic expansion it is now closer to 46 billion light years across. By any measure, this is great. But most cosmologists think that the Universe is much bigger than our visible corner of it. That what we can see is a small part of an unimaginably large universe, that it is not an infinite universe. However, the new paper argues that the observable universe is largely all there is.

In other words, on a cosmic scale, the Universe is very small.

There are many reasons why cosmologists think the Universe is big. One is the distribution of galaxy clusters. If the Universe did not expand beyond what we see, the most distant galaxies would feel the pull of gravity towards our region of the cosmos, but not far from us, leading to asymmetrical clustering. Since the galaxies meet at the same rate in the physical universe. In other words, the observed universe is homogenous and isotropic.

The second point is that space-time is flat. If space-time were not flat, our view of distant galaxies would be distorted, making them appear larger or smaller than they really are. Distant galaxies appear slightly larger due to cosmic expansion, but not in a way that implies a general bending of space-time. Based on the limits of our observation, the flatness of the cosmos means that it is 400 times larger than the visible universe.

Inflation will make the CMB temperature the same. Credit: Nick Strobel

So there is the fact that the cosmic microwave background is almost a perfect black man. There is a slight variation in its temperature, but it is more uniform than it should be. To answer this, astronomers have proposed a period of dramatic expansion just after the Big Bang, known as the first cosmic inflation. We haven’t noticed any direct evidence for it, but the model solves so many universal problems that it is widely accepted. If the model is correct, then the Universe is on the order of 1026 times greater than the visible universe.

So given all this theoretical and observable evidence, how can one argue that the universe is small? It has to do with string theory and swamps.

Although string theory is often presented as a physical theory, it is actually a collection of mathematical methods. It can be used in the development of complex physical models, but it can be mathematical for its own sake. One of the problems of integrating the mathematics of string theory into physical models is that the results will be seen only in the most extreme cases, and we do not have enough observational data to control different models. However, some string theory models seem more promising than others. For example, some models are compatible with quantum gravity, and others are not. Often theoreticians will describe a “swamp” of unpromising theories.

When you separate the promising theoretical fields from the quagmire, what you are left with are theories where early cosmic inflation is not an option. Most string theory models of inflation are swamped. This leads one to ask whether it is possible to build a model of cosmology consistent with observations without early inflation. This brings us to this new lesson.

One way to get around early cosmic inflation is to look at high-resolution structures. The normal normal relationship depends on four physical dimensions, three space and one time, or 3+1. Mathematically you can think of a 3+2 or 4+1 universe, where the world structure can be put into a 3+1 functional structure. This is a common approach to string theory because it is not limited to the standard structure of general relativity. The authors show that under the right conditions, you can build high-quality structures within string theory that are consistent with observations and avoid wet soil. Based on their toy models, the Universe may be a hundred or a thousand times larger than the observed universe. It’s still big, but it’s very small compared to early inflation models.

This is all good speculation, but in some ways it is cosmic inflation. If early inflation is real, we should be able to see its effect on gravitational waves in the near future. If that fails, it might be worth looking more closely at the string theory models that keep us out of the theoretical quagmire.

Reference: Lehners, Jean-Luc and Quintin, Jerome. “A Small Universe.” arXiv preprint arXiv:2309.03272 (2023)

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