# Making sense of distance and speed of expanding universe

1. Jan 16, 2015

### supernova88

I'm trying to reconcile the fact that regions of the universe are expanding faster than light, and that as a consequence the observable universe is far more than 13.7 billion light years across. I trust these are the facts, but I'm stuck figuring out how we know these to be true. I feel like, going off Hubble's Law of roughly 70 km/s/Mpc, we can figure out how fast distant regions of space are expanding as long as we know just how distant they are. However, to find how distant some galaxy at the edge of the known universe is wouldn't we need to know how fast it is receding in the first place. In that way it comes off to me like a chicken-egg scenario, where we need to know velocity to find distance but we need to know distance to find velocity. I'm just hoping someone could smooth this out for me because I'd really like to know how some of these amazing conclusions resulted in the first place. (Also please note I am more of a conceptual physics enthusiast, my math skills are not necessarily astrophysicist-grade, so if you throw a bunch of equations at me, or if you don't explain them thoroughly, I'm probably not going to get it. Thanks.)

2. Jan 16, 2015

### Orodruin

Staff Emeritus
The universe is not really expanding with a speed, it is expanding at a rate. What is happening is that space itself is expanding and it is not due to anything moving inside the space. The space grows at a rate (which can be measured in % per second or equivalent), meaning that the further apart two points are, the faster the distance between them are growing. Compare to stretching a rubber band, when you do this points that are further apart increase the distance between them faster, without anything actually moving on the rubber band (if you were an ant sitting on the rubber band, you are not moving your legs to walk).

3. Jan 16, 2015

### Bandersnatch

Note that you don't need faster than light expansion to get that result but any expansion whatsoever will do. Only in a static (i.e., non-expanding/contracting) universe the size of the observable region would be equal to the age of the universe times the speed of light.

As long as you can conclude that the expansion is a real effect, the size being larger than ~13.8 Gly is a necessary consequence.

If you could only use the redshift to get the recession velocities and distances, then it would be indeed circular. In particular, there would be no way to get the initial relationship at all, bar pure guessing of what the Hubble constant should or could be.
Luckily there are other ways of measuring those.
It outlines the various techniques used for different ranges of distances.

It's very similar to how we get ages of stuff on Earth - you start with tree rings, and move through various radioisotopes, while in parallel checking with the geological strata. In both cases you need some overlap between the techniques and possibly more than one technique for a given distance/age interval.

4. Jan 16, 2015

### marcus

Supernova88, Mr Hubble didn't do us a favor when he got everybody using the awkward unit "km/s per Mpc" for the percentage growth rate of distance. It's misleading because it makes people imagine speeds of motion thru a fixed pre-existing space instead of a percentage growth rate of distances. They get the wrong mental picture.

Google will convert stuff into different units for you. You probably know this already but I'll say it anyway. You just have to type in "15 liters in gallons" and it will tell you what 15 liters is, in gallons. If you aren't familiar with his feature, type it in (without the quotes) and see. Or type in "5 km in miles"

So I'm hoping you will try this (seriously, see if it works for you): type in
" (1/140) percent per million years in km/s/Mpc"

You should get about 70 km/s/Mpc. It does need the parentheses around 1/140.

The point is that 1/140 % per million years is the distance growth rate that people are actually referring to when they say "70 km/s per Mpc".

Recent estimates of the growth rate are slightly down from that. More like 1/144 percent per million years.

5. Jan 16, 2015

### Amaterasu21

Hubble's Law only applies to nearby space! We assume the whole Universe is expanding at the same rate as our local part of space right now, of course, but the expansion rate changes over time, and because light takes a finite time to travel we see distant galaxies as they were millions or even billions of years ago. That means, if we measure the distance to a galaxy 10 billion light years away and measure its recession velocity we see it as it was 10 billion years ago* and therefore get a measure of the Universe's expansion rate and Hubble's constant as it was 10 billion years ago, not today!

Astronomers are therefore not content to simply use Hubble's Law to naively predict the distance to distant galaxies based on their recession speed, and are constantly seeking to measure the distance to far away galaxies using methods independent of Hubble's Law, and to measure their recession velocities. That way we can both measure the distance to distant galaxies and study how the Universe's expansion rate has changed over time.

So your question really boils down to "How can we measure the distances to distant galaxies without needing to use Hubble's Law and break the chicken-and-egg loop?" Ironically, the answer to your question is in your PF username! ^_~ Type Ia supernovae are known as standard candles - objects of known luminosity (all type Ia supernovae explode at the same luminosity, because the explosion is always the same. A type Ia supernova happens in a binary system where two stars of different masses evolve at different rates. One star dies and becomes a white dwarf; the other evolves more slowly and expands to become a red giant. Since the two stars are in close contact, and the red giant star is pretty large and distended, material from this star gets gravitationally attracted to the white dwarf and spirals down onto it. This transfer of mass continues until the white dwarf reaches the Chandrasekhar limit - the upper limit for the mass of a white dwarf, about 1.4 solar masses - collapses and explodes. Because this happens at the same mass for all type Ia supernovae, the physics of the explosion would be identical for all type Ia supernovae and hence they all have the same luminosity). Since we know the luminosity of the supernova, and can measure how bright it appears from Earth, it's a simple calculation to work out how far away that supernova must be. (There are other standard candles too, like Cepheid variable stars, but type Ia supernova are very bright and hence useful for very distant galaxies.) For more about standard candles and using them to get distances to astronomical objects, read this: http://www.astro.ex.ac.uk/people/hatchell/rinr/candles.pdf

Of course, type Ia supernovae are quite rare - they happen once every century or so for any individual galaxy. But there are a LOT of galaxies out there, and if a telescope is focused on a particular patch of sky for long enough, a few type Ia supernovae are bound to happen in it. Doing this for many different patches of sky and finding the distances to many galaxies using this method and measuring their recession rates has helped cosmologists work out how the Universe's expansion rate has changed over time and therefore calculate the age of the Universe. See the Supernova Cosmology Project for an example - they're the group who used supernovae in 1998 to measure the distance to many galaxies and discovered that for the last few billion years the Universe's expansion has been accelerating!

6. Jan 16, 2015

### childe

Ok but can anyone answer this - if the light we see now from the most distant object has taken 10bn years to get to us, and the universe started with the big bang (a single point) after which it has been expanding ever since, then presumably it took some time (say 10bn years?) for this object to get that far from us, in which case once it got there it would take another 10bn years for its light to get to us, which makes the age of the universe at least 20bn years - almost twice current estimates, or have I added 2 and 2 to make 5?

7. Jan 16, 2015

### Bandersnatch

It wasn't a point in space. It happened everywhere throughout the universe, however large it was (including infinite).

8. Jan 16, 2015

### Amaterasu21

It's true that nothing can travel through space faster than the speed of light, but space itself can expand and carry objects with it at relative speeds faster than light. So there's no problem with galaxies we can now see being, say, several billion light years apart when the Universe was only one billion years old, if the light from those galaxies has now only just reached us after travelling for more than 12.8 billion years.

Note also that in an expanding universe the phrase "distance to distant galaxies" can have different meanings. One is the light-travel time distance, or lookback distance - a galaxy appears to be 12 billion light years away, light from it took 12 billion years to reach us, we see it as it was 12 billion years ago. Its lookback distance is 12 billion light years. The other is the comoving distance, which takes into account the expansion of space since the light was emitted. A galaxy may appear to be 12 billion light years away, and we see it as it was 12 billion years ago, but since that light was emitted the space between us and that galaxy has expanded to a much bigger distance - say 30 billion light years. So although the galaxy seems to be 12 billion light years away - and that's how far back in time we look when we see it - it is actually currently 30 billion light years away. (Note that I picked those numbers for examples, I'm not actually sure how far the real comoving distance would be for a galaxy with a lookback distance of 12 billion light years!)

The Universe is 13.8 billion years old by current estimates, so the lookback distance to the edge of the observable Universe is 13.8 billion light years. However, because that "edge" has been carried much farther away from us by the expansion of space since that light was emitted, it's actually about 46 billion light years away now - so that's the comoving distance to the edge of the observable Universe. And note I say "observable", since that isn't the edge of the whole Universe - we don't know how far away that is or if the Universe even has an edge (it probably doesn't). It's just the distance that the age of the Universe, the finite speed of light and the expansion of space allow us to see out as far as (like a kind of cosmic horizon) - we can't yet see beyond it, because the Universe isn't old enough for light beyond it to reach us, but there is almost certainly a whole lot of Universe beyond.

9. Jan 16, 2015

### Amaterasu21

The observable Universe (or any finite volume of space) was concentrated into a point, though. It's just that that point contained all the space in the observable Universe, and wasn't a point "in" the space that now occupies the observable Universe. (This would apply to the whole Universe too, if it was finite - it would have been concentrated into a point at the Big Bang, but that point would contain all the space in the Universe and so the Big Bang would have happened everywhere throughout it. There's no contradiction between the Universe being "point-like" at the Big Bang, and the Big Bang happening throughout all of space, if the Universe is finite! If the Universe is infinite of course, it was infinitely large at the Big Bang and always will be, but the observable Universe and any finite volume of space would have been concentrated into a point at the time.)

(And when I say "point" I actually mean "a very tiny, densely compressed volume," of course. Our lack of a quantum theory of gravity for describing the very earliest moments of the Universe means we can't actually be sure if there ever was a singularity of infinite density, where any finite volume of the Universe would have been point-like, or whether the observable Universe had a minimum size before inflation and its density was incredibly high but not quite infinite.)

10. Jan 16, 2015

### Bandersnatch

Personally, I don't like talking about the BB singularity as if it were a real thing. You have to add so many caveats as to what you don't mean by that, that an uninitiated listener is unlikely to follow and will just take away the sound bite of it being a point, period. Not to mention the rather good possibility of the universe actually being infinite.

But that's even somewhat beside the point. The question asks about the currently observed objects, whose light was emitted long after the universe has grown by a sizeable fraction and long past the inflationary period. All the objects we see, even those farthest away (CMBR) were already separated by millions of light years from the area we now occupy. Personally, I don't think we need to go past the surface of last scattering to straighten the confusion, but then again I can already see how the reader can conflate the recombination with BB singularity after reading my post, so there.

But anyway, you've got comoving distance mixed up with proper distance in post #8. Comoving distance is constant.

(edit: fixed light years)

Last edited: Jan 16, 2015
11. Jan 16, 2015

### Amaterasu21

I agree, the hypothetical Big Bang singularity is a confusing concept. I've had numerous relatives tell me they "don't believe in the Big Bang" or have "heard the Big Bang isn't true anymore," but when I've spoken to them it turns out they all agree that the Universe was in a hot, dense state around 13.8 billion years ago and has expanded since then, they just don't believe in singularities... but I digress. Yeah, the Universe really did have a much smaller scale factor in the past, and the observable Universe really was much, much smaller, regardless of whether or not it was point-like (or whether the Universe as a whole is finite or infinite), and it's this hot, dense early phase we call the Big Bang and not necessarily some hypothetical singularity before that. (Hint hint, popular science authors...)

And ahh, comoving distance is constant? Could you provide some clarification on the difference between comoving and proper distance please? I originally heard the term from here: http://www.atlasoftheuniverse.com/redshift.html Is the author using it incorrectly?

12. Jan 16, 2015

### Bandersnatch

That link is correct, but I think you might have misunderstood what it's saying.

The proper distance is the distance at the time of measurement - you freeze-frame the expansion, take a measuring tape and go find how far a thing is.

The comoving distance, as per the name, expands together with the Hubble flow. Its numerical value is equal (by convention) to the proper distance at the present time.

The two are related by $d(t)=a(t)d_0$ where $d(t)$ is the proper distance (changes with time), $a(t)$ is the scale factor (a function of time as well) and $d_0$ is the comoving distance (a constant).

So, the comoving distance and proper distance are equal at the present time. But if you look at any other time they'll diverge. Something that is now 10 Gly away in terms of proper distance could be said to have been at some time in the past 5 Gly away in terms of proper distance, or 1/2 of $d_0$ in terms of comoving distance - but since it's always known we're talking about fractions of $d_0$, it's the same as saying the distance was half of what it is now, or that the distances in the universe were half as large.

Comoving distance frees you from the need to use actual units for distance, and allows you to just talk in terms of the scale factor. I.e., it was this much closer / will be this much farther.

Another way to think about the comoving distance is as of the relative positions of objects in the expanding universe - they never change. It's like this grid that grows together with the expansion.

(edit: grammar)

Last edited: Jan 16, 2015
13. Jan 16, 2015

### Amaterasu21

Ahh, got you! Thank you!