So how big has the observable universe become since its inception?

The best answer we have comes from something called *redshift*. When a source of light comes from very far away, its wavelength starts to shift towards the red side of the spectrum. This type of Doppler shift was a key indication that the size of the universe is increasing, and can help researchers estimate how much the universe has expanded.

Basically, if we were to find some really old photons and analyze their spectral shift, we’d have a good estimate of how old something is, and how far away it currently lies. The earliest photons we have come from the so-called cosmic microwave background (CMBR), faint cosmic background radiation filling all space which represents the earliest known electromagnetic radiation.

Some of our most accurate estimates of the CMBR come from the Wilkinson Microwave Anisotropy Probe (WMAP), which, along with other estimates, found that farthest observable photons come from 46.5 billion light-years away.

The comoving distance from Earth to the edge of the observable universe is about 46.5 billion light-years 14.26 (gigaparsecs or 4.40×10^{26} meters) in any direction. So, although the light itself might have only traveled for 13.8 billion years, the distance from us to the point it came from is, at present, 46 billion light years away.

This would make the diameter of the observable universe about 93 billion light-years (the equivalent of 28 billion parsecs), assuming that the Earth occupies a relatively central position in the universe.

It should be noted that at the current time, the proper and the comoving distance between the Earth and the edge of the observable universe are defined as equal (for the sake of simplicity). This is merely a convention — at other times, the scale factor was different than 1.

The same measurements described above concluded that at the time the CMBR was emitted, the proper distance was only 42 *million* light-years.

So, to the best of our knowledge, the size of the observable universe is 93 billion light-years across. It is almost certainly bigger than that, but we don’t have any substantial evidence to judge its size outside of that.

However, one statistical estimate carried out by Oxford researchers found that the universe might be 251 times larger than the observable universe, which would put it at 23343 light-years across. That’s truly humbling, and some studies go even beyond that. Estimates for the total size of the universe, reach as high as megaparsecs, as implied by one resolution of the No-Boundary Proposal. Just so you can get an idea of how big that number is, it doesn’t even matter what units of measure you express it in — whether it be nanometers or megaparsecs, the difference would simply get lost in the irrelevant final digits.

### Universal expansion

Universal expansion can be very difficult to wrap your head around, but here’s an easy analogy to help you visualize things.

Think of the universe as a muffin dough. Think of matter inside this space as poppy seeds inside this dough. As the dough is baked, it expands, and the space between all poppy seeds increases — similarly, universal expansion drives matter apart, though the process is only detectable at cosmological scales.

### The shape of the universe

Now, we have some idea of how big the universe is — or rather, we have a lower limit to how big the universe is — but what does it look like?

Most people would probably imagine the universe to be somewhat spherical in shape. Although intuition is hardly reliable in cosmology, a spherical universe is entirely plausible. In General Relativity, space-time is curved, which would imply that there are three possible shapes of the universe:

- flat (zero curvature);
- spherical or closed (positive curvature); or
- hyperbolic or open (negative curvature).

There are also other, more complex shapes which have been proposed, such as a Moebius Strip or its 3D correspondent, a Klein Bottle — where there is no inside or outside, only one surface.

However, more recent evidence suggests that the universe is essentially flat. Temperature measurements of the above-mentioned CMBR would exhibit substantial variations if the universe was curved, but to the best of our ability, we haven’t been able to spot any such variations, which indicates that, to an acceptable range, the universe is essentially flat.

If the universe is indeed “flat”, the math behind General Relativity and universal expansion indicates that it will continue to expand forever, though it’s not clear if this expansion will continue to accelerate indefinitely or will slow down.

However, this doesn’t really tell us anything about how big the universe really is, and there’s an even more puzzling possibility: perhaps the universe is so big that the fraction represented by our observable universe isn’t big enough to exhibit its curvature, much like from our personal perspective, the Earth seems flat, but if you zoom out sufficiently, its curvature becomes evident.

This leaves another important question to discuss.

### Is the universe infinite?

Since we can’t exactly figure out how big the universe is, another possibility emerges: that of an infinite universe.

The two possibilities (of a finite or an infinite universe) raise equally puzzling situations: if the universe is finite, then what could possibly be outside of it, and what exactly is the universe expanding *into*? Is the universe *creating* space? Does that question even make sense?

If the universe is infinite, things get even weirder. How can something that’s not infinitely old be infinitely vast? Can an infinite universe expand? In theory, yes — although it’s very difficult to visualize (and makes the math and physics much trickier). Again, think of the universal expansion not as an “expansion”, but rather a “stretch”, in which all parts of the universe, from the very middle to the periphery, are being pulled apart from each other. But does an infinite universe contain all possible configurations of matter? Is there another you somewhere in the universe? Or even better, is there a version of you that’s immortal, doesn’t need sleep and has cat ears? That is the kind of problem which might emerge from an infinite universe.

### Pi and an infinite universe

A more straightforward issue with an infinite universe is represented by Olbers’ paradox, which states that the darkness of the night sky conflicts with the assumption of an infinite and eternally static universe: if it were truly infinite, then every single bit of the night sky would eventually fall on to a star and would light up, until all the night sky is lit up. Since that doesn’t happen, then the universe isn’t infinite.

The truth is, we don’t know if the universe is finite or infinite, and we may never know. The complexity of the problem seems, at least now, insurmountable. But here’s the good thing: it might not really matter.

Even if the universe isn’t infinite per se, there’s a good chance it is *practically *infinite. This means that some areas might lie so far away from us that we could never reach them. Since according to our current understanding of physics nothing can go faster than the speed of light, considering the accelerating expansion, some areas might simply be mathematically unreachable — we can never interact with them in any way.

The size of the Universe is difficult to define. Because we cannot observe space beyond the edge of the observable universe, we can’t know for sure if it is infinite or not. We have a good idea of how big our observable universe is, but that’s probably just a tiny piece in a much larger puzzle. How big that puzzle is remains an ongoing matter of research — and will likely remain so for years to come.

*Update: edited for typos in age of the universe. *