## The Hubble Bubble.

Janek asks

I would be interested in a further post detailing roughly how we’ve calculated the size of the observable universe.

Okay. Actually I’m more than happy to answer this because the answer is relatively short and it’ll let me bunk off science posts for a week.

So once upon a time there was an astronomer called Edwin Hubble. Hubble’s career is notable for a number of firsts – such as the identification and use of the standard candles known as Cepheid variables found within the Andromeda and Triangulum galaxies to prove that these were indeed galaxies and not merely nebulae as had previously been assumed, thus incidentally proving that the universe extended beyond the bounds of the Milky Way – but the one that ended up getting his name attached to it was the discovery of something called the Hubble constant which basically defines our universe. Astronomers spend a lot of their time nailing down increasingly accurate values for the Hubble constant; part of the motivation for the whole CMB thing is to get better measurements of Ho.

So the Hubble constant is kind of a big deal, and what it is and how it works is best explained by telling the story of how Hubble found it in the first place. After having such success with the Cepheid variable approach to Andromeda and Triangulum (if you need Cepheid variables explained I go over them in one of my first posts here, and the Wikipedia article is here) Hubble decided to see just how many other galaxies he could find with Cepheid variables in them in order to build up a picture of what our universe really looked like. The Cepheids let him measure how far away these particular galaxies were, but while he was observing them he noticed something odd: the light from some of the more distant galaxies displayed a significant degree of redshift. It was already known that galactic redshift was related to their recession velocity thanks to work done by Vesto Slipher a few years earlier, and so Hubble was able to make a graph of galactic distance versus recession velocity that looked much like the following:

It’s a straight line relationship (albeit one with a fair amount of scatter), which is convincing evidence that the recession velocity of a particular galaxy is directly proportional to its distance away from . In other words,

where v is the recession velocity of the galaxy, d is its distance from us, and Ho is the Hubble constant. The expression above forms Hubble’s law, which states that the further away from us something is the faster it will be moving – and since that movement is caused by the expansion of space, Hubble’s law is effectively a relationship which governs that phenomenon. This means that what exactly the precise value of the Hubble constant is is going to have a profound impact on our views of how the universe is expanding, which is why scientists are so interested in obtaining increasingly accurate measurements of it. It also incidentally allows us to get a rough idea of galactic distance by measuring the redshift, converting it into a recession velocity, and plugging it into Hubble’s law along with the current value of the Hubble constant (67.80 ± 0.77 km s-1 Mpc-1 as of the most recent measurements obtained by the Planck probe).

So in theory when we look at things we have a fairly good way of figuring out how far away they are from us. All we have to do is find the thing that’s furthest away, plug its redshift into Hubble’s law, and from that calculate the approximate radius of our observable universe, right? Unfortunately — as with most things in astronomy – the reality is nowhere near that simple. Whenever you read an article reporting the discovery of the most distant astronomical object yet discovered, that article will likely quote two things: the object’s redshift, which is a thing that can be directly measured via observation, and its age, which can be reliably calculated from its redshift. What it won’t quote, unless it’s been written by an idiot, is its distance from us. This is due to several factors which complicate Hubble’s law immensely, most notably:

• That the simplified version of the law I described above – which incidentally is the one we teach to reasonably intelligent people up to and including undergraduate level1    – assumes that the redshifted light we see from galaxies moving away from us is caused by a simple Doppler effect; that is, that the galaxies are moving away from us through space, like a boat sailing on the ocean. What’s actually happening is that the space itself is expanding and carrying that boat away from us on a tidal wave, which requires a far more complex treatment of the redshift.
• That the rate of galactic expansion has been constant and unchanging throughout its entire history. This is not true, as we now think that the universe is accelerating in its expansion. You know that value of Hubble’s constant we calculated just this year using the Planck probe? That’s the value of Hubble’s constant now. We have little to no idea what the value of Hubble’s constant was ten billion years ago, and the various cosmological models that attempt to establish this differ wildly in their predictions of how it’s changed over time.

These two factors together not only make the use of galactic redshift to calculate distance a rather iffy proposition at the best of times, but that second one also makes it effectively impossible to gauge the distance of the really old stuff we find. And if we can’t put an accurate number on those distances, this means it’s impossible to directly measure the volume of our observable universe.

If that’s the case, though, then why do astronomers throw around a precise number for the radius of the observable universe (currently about 46 billion light years)? It’s because they’re not using the term observable in the same way that you (or I) might. To them, “observable” does not mean “Can we see it right now?” Instead, the observable universe is simply the radius inside which light emitted from objects at some point over the entire history of the universe could theoretically reach us here on Earth. It doesn’t matter if the light actually does get here or not, or whether somebody manages to detect it, or whether we can make sense of what we eventually see; if the light has the potential ability to reach us, then the part of the universe that would hypothetically emit it falls within the bounds of the observable universe.

This simplifies the calculation of the radius of the observable universe immensely; instead of trying to establish actual physical boundaries you simply dial things back all the way to the oldest thing that could possibly exist and be observed and try to derive a distance measurement to that. In the case of our universe this happens to be the cosmic microwave background radiation, which is a collection of extremely redshifted particles released at the moment of photon decoupling2. That 46 billion light-year number is derived from our observations of the surface of last scattering, a collection of points in the sky where photons from the CMB are only just now reaching us here on Earth. The great advantage of using the CMB to calculate this radius is that it isn’t just one object; since it exists over the entire sky it provides an awful lot of data which allows astronomers to average out those huge uncertainties in using redshift to gauge distance I described above. This means that it’s a reasonably solid number, although there’s no reason a more detailed observation of the CMB wouldn’t cause it to change in future.

So that’s how we arrived at a definition for our observable universe. There’s stuff inside it that we haven’t seen — and likely never will – because our instruments aren’t good enough, but that doesn’t change the fact that we could see it with sufficiently advanced equipment. It’s possible that the boundaries of the observable universe could move outwards if we figure out a way to see stuff without relying on electromagnetic radiation (observations of neutrino emissions and gravity waves could allow us to look back beyond the moment of photon decoupling, for example) but I wouldn’t hold your breath; that stuff is very definitely future science.

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1. And also incidentally is the reason this post is suddenly changing direction, because I had literally no idea it was wrong.
2. I might go into more detail on this later on, but: during the early stages of existence up until about 300,000 years after the Big Bang, things were still sufficiently hot and dense enough that the universe was opaque to photons. This means that radiation as we understand it, including light, could not travel through space, and so peering back past that 300,000 year barrier is going to be impossible using our current observational methods because no observable light actually existed prior to that moment. The point where photons became able to travel about the universe freely is known as photon decoupling, and it’s this first primordial batch of radiation that forms the cosmic microwave background.

## 11 thoughts on “The Hubble Bubble.”

1. Gap Gen says:

Yes, I never understood the expansion of space either until undergrad, at which point I read about the scale factor and was like “ohhh…” I never really understood the balloon example, either (doesn’t help that it looks like a spherical explosion expanding, which the Big Bang is not). Perhaps with computer graphics it’s easier to just draw a grid that’s getting bigger and bigger, and have galaxies sitting on top of it while staying the same size, but that’d probably confuse someone too.

• Hentzau says:

You have to find a way to separate space from the galaxies within it in order to explain expansion. The grid idea is one that I intuitively understand, and it would probably work as long as you explained that the reason galaxies aren’t expanding too is because they’re gravitationally bound.

• Gap Gen says:

Yeah, I guess this is the thing about the big rip, eventually the expansion overcomes the binding energy of the galaxy and the stars fly apart. Not that they’ll still be burning by that point, I suppose.

2. Glen says:

This is fascinating stuff. Here’s what always confuses me:

“…so peering back past that 300,000 year barrier is going to be impossible using our current observational methods…”

How can we “peer beyond” what has already happened? (Terrible analogy ahead) It’s a bit like saying: if the universe is an ocean, and we’re a tiny plankton in the year 2013, we can develop a periscope powerful enough to see Magellan’s voyage through the Pacific. I understand that much of the universe we “see” today isn’t actually there at all, given the length of time the light waves took to get to us, but how can you ever expect to “see” events that we* were presumably a part of when they happened (300,000 years after the big bang, for instance)? I can’t wrap my head around that.

*By “we” I mean our particles and dust and such, not humans or our solar system or anything.

• Hentzau says:

I might do another post about this next week to round things off (especially with the whole looking back into earlier and earlier regions of the universe thing) but the quick answer is that it’s possible for space to expand faster than light. During the first second of the universe’s existence this is exactly what happened during inflation; to a hypothetical observer it would have appeared as though the things they were looking at were all suddenly disappearing as the rapid expansion during the inflation drove them beyond the observable horizon. Then things slowed down to a more sedate pace, and our observable horizon gradually started to move outwards as light from the areas that had been thrust out beyond it started to reach us again.

Fast forward to the present day, and we’re just now “rediscovering” areas of the universe that we’ve been out of touch with ever since that first second. This is how we can see back to (and possibly past) photon decoupling at the 300,000 year point; this happened *after* inflation, and so there are regions of the universe where it took place beyond our observable horizon — so we were never part of those events in the first place. It’s the light from those regions that is reaching us now and is forming the cosmic microwave background radiation.

This isn’t the best explanation of a very counterintuitive concept, so do feel free to enquire further if you’re still puzzled by it all.

3. About this space expansion thing… As far as I understand the distance between any two points is constantly (but slowly) multiplies. Does it affects even atomic length? I mean is every electron goes farther and farther from it’s core? Or is it space expansion only covers macrophysics?

And so here goes even more mindblowing thing: if the first is right, how does it affect all those subatomic processesand powers? If the latter, is the speed of light becomes more insignificant each minute or does it scale with space?

• Hentzau says:

Your first point is an interesting one because of the accelerating expansion of the universe. Currently the four fundamental forces — the glue keeping atoms and galaxies together, such as electromagnetism and gravity — easily counteract the expansion of the universe, which is why galaxies, stars, planets and people are not being torn apart as the space beneath them expands. If the expansion continues to accelerate, though, there may come a time where this is no longer the case and things literally begin to get ripped apart; look up the Big Rip on wikipedia for the general apocalyptic idea behind this. http://en.wikipedia.org/wiki/Big_Rip

(Note: the Big Rip is conjecture at the moment and is in no way a legit thing. It’s just useful for illustrating how expansion could possibly grow out of control.)

As to your second point, the speed of light is a constant, and it’s still a very large number. It will always govern all the processes that matter to us on human scales — so in a billion years time subatomic processes and whatnot will still function exactly the same way as they do now. However when you look at things on a universal scale the speed of light could begin to pale into insignificance when compared to the speed of expansion of space, leading to the rather comical Big Rip scenario referred to above.

• Yeah, I’ve heard about this Big Rip before and it looks like the most absurd end-of-the-world scenario. If you an atheist you may believe that judgement day and archangels with trumpets is bollocks, you’d probably imagine Sun exploding (but by that time we may colonize the universe or something so no big deal), or maybe something like a new big bang creating a new universe on place of other. But this Big Rip is as silly as you can get. Suddenly everything disintegrates, puff. Even atheist tend to believe life has some meaning to it, and that’s why I think it’s so hard to believe in this end of the universe scenario.

Also, if the universe is big enough, there should be a distance that you could never reach or see, right? The light that travels this distance would go with the same speed the distance is getting bigger. So there should be some theoretical size of universe beyond which we’ll never would see anything, am I right?

• Hentzau says:

I was going to talk about this next week, but yeah. The Hubble constant seems to increase the further out you go, so there’s something called the Hubble volume which marks the point at which space is expanding faster than light can travel in the opposite direction, and so no light emitted from outside that volume will ever reach Earth.

(This is different from the observable universe in that the observable universe covers all light that has been emitted over the history of the universe. The Hubble volume on the other hand covers light that is emitted from objects *now*, and as such is about a third the size of the observable universe.)

4. Glen says:

I think I need to go back and re-read your inflation post. I didn’t really understand the magnitude of it, I guess. I imagined it as more gradual; not so rapid that the light could be just now reaching us from “The Great Decoupling*”, which was incredibly early in the grand scheme of the universe. It’s sad to know that chances are we won’t ever be admitted into the Intergalactic Federation, as it more than likely doesn’t exist anymore.

Damn you space. Damn you for inflating us out of our greatest future-accomplishment!

On a more serious note: By your post above I guess it’s safe to assume that inflation has stopped, or at least slowed to the point of nearly stopping? Perhaps this is a good sign; an omen for those of us that naively hope for an endless cycle of Big Bang and “Big Crunch”. I mean, even with the infinitesimally small odds, at least it gives me another shot at this incredible ride, right? Hell, I was here once, that’s for sure!

*I think that’s a much more exciting moniker. You can use that around the office if you like.

• Gap Gen says:

Note that “inflation” only refers to the super-fast expansion at the start of the universe, rather than the slower expansion we see today.

As for the 2nd part, we think the expansion of the universe is accelerating, which is effectively what “dark energy” is – an extra energy term in the equations designed to make the observations fit the theory. So a Big Crunch is unlikely unless our theory is wrong, which is entirely possible, though we’d have to explain why the theoretical fit to the data (with dark energy included) is so good.