The observable universe

[I suggest reading my earlier post, The Big Bang, before this one.]

The observable universe (OU) is the part of the universe that we can, at least in principle, observe, from a designated vantage point at a given place and time. This post is my attempt to figure out in more detail exactly what the OU could be, and especially how time might factor into it.

I’ll assume our vantage point is present day Earth, and I’ll assume the age of the universe is exactly 13.8 billion years. I’ll use the term “NOW” as an abbreviation for age 13.8 billion years. I’ll abbreviate “million years” as “My”, and “billion years” as “By”.

Imagine every object in the universe has a big visible neon clock on it, displaying the age of the universe from its own perspective. The light emitted by these clocks travels at the speed of light, of course.

Technical note: The clocks are smart enough to correct for relativistic time dilation. A clock reports the apparent age of the part of the universe it’s in, not the clock’s own personal age. Two nearby objects will therefore always have about the same clock age.

From Earth, we look out and see lots of clocks showing various ages. The latest of all the ages, 13.8By (“NOW”), is shown by Earth’s own clock. The Moon’s clock shows a number that we interpret as NOW minus 1.3 seconds. The Sun’s clock shows NOW−8.3min. The Andromeda galaxy is 2.54 million light years away, so its clock reads NOW−2.54My, or 13.79746By. As we look at objects that are more and more distant, their clock ages get earlier and earlier. We also notice that, generally speaking, the more distant an object is, the slower its clock appears to tick. This is due to the doppler effect, caused mainly by the expansion of the universe.

As of this writing, the earliest known galaxy is reportedly one known as GN-z11, whose clock reads about 400My.


The particle horizon

The boundary of the OU is called the particle horizon. It is defined as the greatest distance from which particles could have reached Earth since… well, since when exactly? The Big Bang? Almost, but not quite.

It’s pretty well established that something called the inflationary epoch happened for a brief moment in the first fraction of a second of the universe’s existence — from very roughly age 10-36 to 10-32 seconds. I admit I don’t understand the implications of this epoch very well. Apparently, during the inflationary epoch, the universe was expanding so fast that objects were being carried out of that era’s equivalent of the OU. So, to define the modern OU in a sensible way, we exclude any part of the universe that has not been observable since the end of the inflationary epoch. Otherwise, the definition of “observable universe” would imply a universe very much larger than what we can actually observe.

The Cosmic Microwave Background Radiation

The oldest light we can see is that of the Cosmic Microwave Background Radiation (CMBR), whose clock reads about 370,000y. The OU actually extends back to earlier ages, even though we cannot see anything from those ages — at least not using light. It might be possible to “see” beyond the CMBR using gravitational waves or neutrinos, but that’s not the point. The OU is not defined based on what we can actually observe in practice; it’s based on what could be observed in principle, without breaking any fundamental laws of physics like the speed of light. The CMBR is a useful landmark, but it’s not really important from a strictly theoretical perspective.

The CMBR is often described as being “all around us”, which is technically true, but misleading. The light from the star Sirius is also all around us (except where it is blocked by something), yet we wouldn’t describe Sirius as being all around us. The CMBR is more like a very distant wall: the inner surface of a huge sphere, with us at the center, and containing all the other visible objects in the universe.

Future past

A strict way to define the OU is that it is essentially just the past light cone of Earth: the surface of spacetime containing all the objects at the universe-ages that we see them from Earth. The objects on this surface have ever-decreasing neon clock ages going all the way back to nearly age zero.

Andromeda@{NOW−2.54My} is unambiguously in the OU. But is Andromeda@NOW in the OU? Andromeda at that age is not observable yet, but it eventually will be. (Or at least, its region of space will be. We can’t be absolutely certain that Andromeda@NOW will exist. For all we know, the Andromeda galaxy was eaten by a herd of star goats thousands of years ago.)

If we loosen our definition of OU somewhat, we can include the “future past” versions of Andromeda: Andromeda@{NOW−2.54M} through Andromeda@NOW.

The cosmic event horizon

Because the expansion of the universe is accelerating, the @NOW version of objects more distant than a certain horizon, called the cosmic event horizon, will never be visible from Earth. Over a huge amount of time, observers on Earth will see them get dimmer and dimmer, and will see their clocks run slower and slower, each one approaching some asymptotic limiting time earlier than NOW.

Imagine a galaxy named GalaxyA, whose clock reads 6By, and whose limiting age is 10By — the latest clock time that will ever be visible from Earth. We could reasonably add GalaxyA@6BY through GalaxyA@10BY to our list of things in the OU. But I think it’s a little dubious to include later versions, like GalaxyA@NOW, since those versions will never be observable from Earth.

The cosmic event horizon is currently about 16 billion light years away, but I do not know how to calculate what the clock of an object on that horizon currently reads.

Is the observable universe getting larger, or smaller?

People sometimes ask whether the OU is getting larger, or smaller. It’s currently getting larger in size, by any reasonable way of measuring its size. But I think what is usually meant by that question is whether it’s getting “more stuff” in it, or getting “less stuff” in it as distant objects move out of it.

It seems strangely difficult to get a straight answer to this question. Some experts say things that clearly imply “more”, while others clearly imply “less”.

But I’m pretty sure I know the answer: The OU is currently getting more stuff in it. This will continue to be the case for as long as we can detect the CMBR.

If we look into distance space, and watch for a long time, we see the CMBR receding, leaving the seeds of new galaxies in its wake. This has always been the case, ever since the CMBR formed. Therefore, if anything has ever left the OU, it would have to have happened before the CMBR formed. That’s long before any galaxies formed, so at the very least, we can definitely conclude that no galaxies have ever left the OU.

Over time, we see distant galaxies getting dimmer from our viewpoint. So, a particular galaxy may well have moved out of the range of a particular telescope. But just get a better telescope, and you’ll be able to see that galaxy again. Or at least, there’s nothing in principle preventing that galaxy from being observed. Again, the OU is all about what is observable in principle, not about what can be seen at a particular level of telescope technology.

The distant future

In the very distant future, the CMBR will get so dim that we cannot detect it, even in principle. The wavelength of each of its photons will be stretched to the point where it is larger than any possible detection device. At about that time, the OU will start getting less stuff in it, for the first time since the end of the inflationary epoch. It will eventually get smaller in actual size, not just with respect to the amount of stuff in it. We don’t yet know what the eventual fate of the universe will be, but at the very least our OU will someday be reduced to the remnants of our Local Group of galaxies.

Beyond the observable universe

The OU seems to be part (probably a very small part) of a “greater universe” that exists mostly beyond it. This makes sense: The OU is getting more stuff in it, and that new stuff has to be coming from somewhere.

Actually, it’s not inconceivable that the greater universe could be smaller than the OU. If so, then some of the galaxies we see are in fact duplicate images of other galaxies we see. However, it’s my understanding that observational evidence has pretty much ruled out this possibility.

And since the size of the OU is always changing, it would be a total coincidence if it were currently exactly the same size as the greater universe.

Only a finite amount of the greater universe will ever enter our OU. I’d argue that the forever-unobservable greater universe beyond this has only a tenuous claim on even “existing” in any meaningful sense. I hope to discuss this in more detail in a future post.

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