Have a theological question?

The honest answer is we don't know if the Universe is finite or infinite, but we do know some solid numbers about the part we can observe.

The observable Universe

This is the part we can actually see, limited by the speed of light and the age of the Universe (about 13.8 billion years).

• Radius: about 46.5 billion light-years
• Diameter: about 93 billion light-years

You might expect the radius to just be 13.8 billion light-years since that's how long light has had to travel, but the Universe has been expanding the whole time, light was enroute. So the most distant light we detect today, like the cosmic microwave background, came from matter that's now much farther away than 13.8 billion light-years, as space itself stretched out during the journey.

Beyond the observable part

The observable Universe is just the part light has had time to reach us from just the limit of what we can currently see. It's centred on us only in the trivial sense that everyone, everywhere, would see their own observable bubble centred on themselves.

The total Universe is almost certainly much bigger than the observable part, plausibly hundreds of times larger by some estimates, or possibly infinite. Measurements of its geometry (how flat space is) put it consistent with being flat and infinite, but current data can't fully rule out that it's finite and just very large, curving back on itself in a way too subtle to detect yet.

So in short:

• Observable Universe: ~93 billion light-years across; a hard, measured number.
• Whole Universe: unknown, possibly infinite.

How we measure the 46.5 billion light-year figure

It comes from combining two things:

• The age of the Universe (~13.8 billion years), determined mainly from the cosmic microwave background (CMB), the leftover radiation from about 380,000 years after the Big Bang, when the Universe first became transparent to light. Its properties let cosmologists pin down the age very precisely.

• The expansion history of the Universe, described by the Friedmann equations from general relativity. We know how fast the Universe has expanded at different points in its history; first decelerating due to gravity, then accelerating due to dark energy, based on how much matter, dark matter, and dark energy it contains (these proportions come from CMB measurements and observations of supernovae, galaxy clustering, etc.).

Feed the expansion history into the equations, and you can calculate: for light that left a distant point 13.8 billion years ago and is only now reaching us, how far away is that point today, after accounting for all the stretching of space along the way?

The answer comes out to about 46.5 billion light-years. It's a calculation, not a direct measurement, but it rests on quantities (age, expansion rate, matter/energy content) that are each independently measured and cross-checked.

Flat vs. curved geometry

Three basic possibilities for the shape of space itself:

• Positively curved (closed), like the surface of a sphere; finite, no edge, and if you travelled far enough in one direction you'd loop back around.
• Negatively curved (open), like a saddle shape; infinite.
• Flat, also infinite, like ordinary Euclidean space extended forever.

Which one it is depends on the total density of matter and energy compared to a critical density. Astronomers measure this by looking at the CMB: tiny temperature fluctuations in it form patterns of a characteristic size, and how large those patterns appear to us depends on whether space is curved (which would magnify or shrink them, like a funhouse mirror) or flat.

The result, from missions like Planck: the Universe is flat to within about a 0.4% margin of error. That's stunningly close to flat, suspiciously close, which is actually one of the motivations for the theory of cosmic inflation, a period of extremely rapid expansion in the first fraction of a second that would naturally flatten out any initial curvature, the same way inflating a balloon to enormous size makes its surface look locally flat.

But "flat within 0.4%" doesn't rule out a very slight curvature that's just too subtle for current instruments to detect; meaning we can't fully exclude a Universe that's finite but astronomically larger than the observable part.

About Coram Deo

Coram Deo — before the face of God. This blog reflects on Scripture, world events, science, music, psychology, and the human mind — always through the lens of Christian faith. All of life is lived before the face of God.