# How Big is the Observable Universe?

One question that often gets asked is "How big is the universe?" Unfortunately, the answer to this question is a big fat "No one knows," which may provide an interesting starting point for discussion, but is hardly a satisfying answer for anyone.

A question that we can answer, however, is "How big is the observable universe?" And, in fact, we can not only ask this question, but can even do a pretty good job of answering it.

What a difference a word makes!

The Observable Universe vs. The Universe

This distinction between the "universe" and the "observable universe" is potentially an important one. Philosophers and scientists used to think (following the lead of Aristotle) that the universe was eternal, and many suggested that it was probably infinite in size as well. As such, the "observable universe" was in fact the universe as a whole.

There is a problem with this, though. If the universe were indeed infinite, then everywhere that you looked, you would expect there to be stars there. Instead of a dark night sky, you would see a bright sky full of light coming from all directions. This bizarre conclusion was known as Olber's paradox (and is well described in Jim al-Khalili's book Paradox: The Nine Greatest Enigmas in Physics).

The solution to the paradox is that the space we can see is not infinite. In fact, modern physics puts definite limits on how much can be seen, based on the evidence supporting the Big Bang theory and the rules of Einstein's theory of relativity ...

specifically that the speed of light is constant. Judging from the observed expansion rate of distant galaxies, we can estimate roughly how far back in time all of the matter was at a single point. This gives us, roughly speaking, an age to the universe. Since the speed of light is constant (according to relativity), then that means light that is further away from us than this number of lightyears hasn't had enough time to reach us yet.

Theoretical physicist Max Tegmark, in his book Our Mathematical Universe:  My Quest for the Ultimate Nature of Reality, presents the following definition of "Our Universe":

The part of physical reality we can in principle observe.

Dr. Tegmark then elaborates a bit:

If we ignore the quantum complications [...], the following universe definition is equivalent.

The spherical region of space from which light has had time to reach us during the 14 billion years since our Big Bang [...]

In the past chapters, we also referred to this region as our observable universe. Geekier-sounding synonyms that are popular with astronomers are our horizon volume, or the region within our particle horizon.[...]

Given that other universes may exist, I find it a bit arrogant referring to our own as the universe, so I try to avoid using that term altogether.

The observable universe is sometimes used synonymously with the Hubble volume, which was one of the first approximations for the size of the observable universe. It was based directly on the galactic expansion rate observed by Edwin Hubble in 1927, with the idea being that it represented the volume of space at which any galaxy would be moving away from Earth at the speed of light ...

and, therefore, could never have any interaction with us.

What was not clear was exactly what this meant. Some people thought that this distance represented some sort of distant singularity, which contained our universe and from which nothing could escape. The Hubble volume would continue expanding, but it would still contain all of the same stuff. Recent evidence in support of dark energy, however, calls this into question. If dark energy is indeed causing an acceleration between different far-flung regions of space (which is what it appears to do), then eventually galaxies that are near the edge of the Hubble volume would in fact accelerate their way outside the Hubble volume, if given enough time.

Size of the Observable Universe

How does one determine the size of the observable universe? The size has changed over the years, to be sure, as our technology has advanced so that we've been able to see more and more of the observable universe.

It is important to remember that when we talk about how far we can see in astronomical terms, we are also talking about looking backward in time. Roughly speaking, if we look at a star that is 10 billion lightyears away from us, then we are seeing the light that left that star 10 billion years ago. (This is straight from the definition of a lightyear: the distance light travels in a year.)

Using the theory of relativity, physicist George Gamow and colleagues calculated the expected temperature of the cosmic microwave background radiation, which they predicted would fill all of space ... a remnant of the energy left over from when the quark-gluon plasma that was formed in the early moments of the Big Bang cooled enough to form into protons and neutrons and, therefore, into atoms and stars.

This cosmic microwave background radiation has indeed been observed throughout the universe (and, in fact, this research earned the 2006 Nobel Prize in physics), and provides an evidence-based measure against which the theoretical predictions regarding cosmology can be evaluated. (Remember that, ideally, scientists do like to check their theories against the evidence.) The result of this is that the universe is about 13.8 billion years old (give or take a few tens of millions of years), so we might expect the observable universe to be a sphere roughly 27.6 billion years across, right?

Wrong!

What this approach fails to take into account is that the matter in the universe isn't just expanding in spacetime, but also spacetime itself is expanding, according to the theory of general relativity. In fact, according to the modification of the Big Bang theory known as inflation theory, the early universe was accelerating extremely rapidly. In fact, even today, the edge of the observable universe is actually expanding about 6 times faster than the speed of light. (Objects in spacetime cannot move faster than the speed of light, but spacetime itself can move faster than that.)

When all of this is taken into account and carefully analyzed, the actual size of the observable universe is actually closer to 93 billion lightyears in diameter!

In other words, when an astronomer takes the most sophisticated telescope and looks at the farthest thing that can even in theory be seen, it would be located a bit over 46 billion lightyears away ... even though there's been only 13.7 billion years for that light to reach us!