If you look farther and farther away, you also look farther and farther into the past. The earlier you go, the hotter and denser, as well as less-evolved, the Universe turns out to be. The part that we can see is limited and finite. But what about what lies beyond? Image credit: NASA / STScI / A. Feild (STScI).

Ask Ethan: Is the Universe infinite or finite?

Either possibility offers a tremendous existence, but philosophically, there’s so much more to think about.

“If the doors of perception were cleansed every thing would appear to man as it is, Infinite. For man has closed himself up, till he sees all things thro’ narrow chinks of his cavern.” -William Blake

13.8 billion years ago, what we know as our Universe began with the hot Big Bang. It’s been expanding and cooling ever since, up through and including the present day. From our point-of-view, we can look back some 46 billion light years in all directions, thanks to the speed of light and the expansion of space. Although that’s a huge distance, it’s not infinitely large. But that’s merely what we can see. What lies beyond that, and could that be infinite? That’s what Buck wants to know, as he asks:

What I’d like to see discussed whether the universe is finite or infinite, and why it might be either. I’ve seen some limited discussion by [Sean Carroll] and [Lisa] Randall to the effect it could be either. We just don’t know.

It’s true that we don’t know whether it’s finite or infinite, but we know a lot more than what we see within the part that’s observable to us.

Looking out at more and more distant objects in the Universe reveals them to us as they were farther back in time, going all the way back to before there were atoms, all the way to the Big Bang. Image credit: NASA, ESA, and A. Feild (STScI).

As we look to greater distances, we also wind up looking back in time. The nearest galaxy, some 2.5 million light years away, appears to us as it was 2.5 million years ago, because the light requires that much time to journey to our eyes from when it was emitted. More distant galaxies appear as they were tens of millions, hundreds of millions or even billions of years ago. As we look ever farther away in space, the light we see from the Universe comes from its progressively younger days. So why not go all the way back to the beginning: to the light that was emitted 13.8 billion years ago? We’ve not only looked, but we’ve found it: the cosmic microwave background, which is the leftover glow from the Big Bang.

Only a few hundred µK separate the hottest regions from the coldest, but the way the fluctuations correlate in scale and magnitude encodes a tremendous amount of information about the early Universe. Image credit: ESA and the Planck Collaboration.

What we find is that the Universe was almost perfectly uniform back then, but some regions were more or less dense than average, by only 1-part-in-30,000. That’s enough to grow into the stars, galaxies, galaxy clusters, and cosmic voids we see today. But these early imperfections that we see from this cosmic snapshot encodes an incredible amount of information about the Universe. One such piece of info is a startling fact: the curvature of space, as best as we can tell, is completely flat. If space were positively curved, like we lived on the surface of a 4D sphere, distant light rays would converge. If space were negatively curved, like the surface of a 4D saddle, distant light rays would diverge. Instead, distant light rays move in their original direction, with the fluctuations we have indicating perfect flatness.

The magnitudes of the hot and cold spots, as well as their scales, indicate the curvature of the Universe. To the best of our capabilities, we measure it to be perfectly flat. Image credit: Smoot Cosmology Group / LBL.

From constraints arising from both the cosmic microwave background and the large-scale structure of the Universe combined, we can conclude that if the Universe is finite and loops back in on itself, it needs to be at least 250 times the extent of the part we observe. Because we live in three dimensions, 250 times the radius means (250)3 times the volume, or more than 15 million times as much space. But, big as that is, it still isn’t infinite. A lower bound of the Universe being at least 11 trillion light years in all directions is tremendous, but it’s still finite.

The observable Universe might be 46 billion light years in all directions from our point of view, but there’s certainly more, unobservable Universe just like ours beyond that. Image credit: Wikimedia Commons users Frédéric MICHEL and Azcolvin429, annotated by E. Siegel.

There’s reason to believe our Universe is even bigger than that, though. The hot Big Bang might mark the beginning of the observable Universe as we know it, but it doesn’t mark the birth of space and time itself. Before the Big Bang, the Universe underwent a period of cosmic inflation. Instead of being filled with matter and radiation, and instead of being hot, the Universe was:

  • filled with energy inherent to space itself,
  • expanding at a constant, exponential rate,
  • and creating new space so quickly that the smallest physical length scale, the Planck length, would be stretched to the size of the presently observable Universe every 10–32 seconds.
Inflation causes space to expand exponentially, which can very quickly result in any pre-existing curved space appearing flat. Image credit: E. Siegel (L); Ned Wright’s cosmology tutorial (R).

It’s true that in our region of the Universe, inflation came to an end. But there are three questions we don’t know the answer to that have a tremendous influence on how big the Universe truly is, and whether it’s infinite or not.

Inflation set up the hot Big Bang and gave rise to the observable Universe we have access to, but we can only measure the last tiny fraction of a second of inflation’s impact on our Universe. Image credit: E. Siegel, with images derived from ESA/Planck and the DoE/NASA/ NSF interagency task force on CMB research.

1.) How big was the region of the Universe, post-inflation, that created our hot Big Bang? Looking at our Universe today, at how uniform the Big Bang’s leftover glow is, at how flat the Universe is, at the fluctuations stretched across the Universe on all scales, etc., there’s quite a bit we can learn. We can learn the upper limit to the energy scale at which inflation occurred; we can learn how much the Universe must have inflated; we can learn a lower limit how long inflation must have gone on for.

But the pocket of the inflating Universe that gave rise to us could be much, much bigger than that lower limit! It could be hundreds, or millions, or googols of times larger than what we can observe… or even truly infinite. But without being able to observe more of the Universe than we can presently access, we don’t have enough information to decide.

If inflation is a quantum field, then the field value spreads out over time, with different regions of space taking different realizations of the field value. In many regions, the field value will wind up in the bottom of the valley, ending inflation, but in many more, inflation will continue, arbitrarily far into the future. Image credit: E. Siegel / Beyond The Galaxy.

2.) Is the idea of “eternal inflation” correct? If you consider that inflation must be a quantum field, then at any given point during that phase of exponential expansion, there’s a probability that inflation will end, resulting in a Big Bang, and a probability that inflation will continue, creating more and more space. These are calculations we know how to do (given certain assumptions), and they lead to an inevitable conclusion: if you want enough inflation to occur to produce the Universe we see, then inflation will always create more space that continues to inflate compared to the regions that end and produce Big Bangs.

While our observable Universe may have come about from inflation ending in our region of space some 13.8 billion years ago, there are regions where inflation continues — creating more and more space and giving rise to more Big Bangs — continuing to the present day. This idea is known as eternal inflation, and is generally accepted by the theoretical physics community. How big, then, is the entire unobservable Universe by now?

Wherever inflation occurs (blue cubes), it gives rise to exponentially more regions of space with each step forward in time. Even if there are many cubes where inflation ends (red Xs), there are far more regions where inflation will continue on into the future. The fact that this never comes to an end is what makes inflation ‘eternal’ once it begins. Image credit: E. Siegel / Beyond the Galaxy.

3.) And, finally, how long did inflation go on prior to its end and the resultant hot Big Bang?We can only see the observable Universe created by inflation’s end and our hot Big Bang. We know that inflation must have occurred for at least some ~10–32seconds or so, but it likely went on for longer. But how much longer? For seconds? Years? Billions of years? Or even an arbitrary, infinite amount of time? Has the Universe always been inflating? Did inflation have a beginning? Did it arise from a previous state that was around eternally? Or, perhaps, did all of space and time emerge from nothingness a finite amount of time ago? These are all possibilities, and yet the answer is untestable and elusive at present.

A huge number of separate regions where Big Bangs occur are separated by continuously inflating space in eternal inflation. But we have no idea how to test, measure or access what’s out there beyond our own observable Universe. Image credit: Ozytive — public domain.

From our best observations, we know that the Universe is an awful lot bigger than the part we can observe. Beyond what we can see, we strongly suspect that there’s plenty more Universe out there just like ours, with the same laws of physics, the same types of physical, cosmic structures, and the same chances at complex life. There should also be a finite size and scale to the “bubble” in which inflation ended, and an exponentially huge number of such bubbles contained within the larger, inflating spacetime. But as inconceivably large as that entire Universe — or Multiverse, if you prefer — may be, it might not be infinite. In fact, unless inflation went on for a truly infinite amount of time, or the Universe was born infinitely large, the Universe ought to be finite in extent.

As vast as our observable Universe is and as much as we can see, it’s only a tiny fraction of what must be out there. Image credit: NASA, ESA, R. Windhorst, S. Cohen, and M. Mechtley (ASU), R. O’Connell (UVa), P. McCarthy (Carnegie Obs), N. Hathi (UC Riverside), R. Ryan (UC Davis), & H. Yan (tOSU).

The biggest problem of all, though? It’s that we don’t have enough information to definitively answer the question. We only know how to access the information available inside our observable Universe: those 46 billion light years in all directions. The answer to the biggest of all questions, of whether the Universe is finite or infinite, might be encoded in the Universe itself, but we can’t access enough of it to know. Until we either figure it out, or come up with a clever scheme to expand what we know physics is capable of, all we’ll have are the possibilities.

Starts With A Bang is now on Forbes, and republished on Medium thanks to our Patreon supporters. Ethan has authored two books, Beyond The Galaxy, andTreknology: The Science of Star Trek from Tricorders to Warp Drive.