Observational Evidence for the Expansion of the Universe

[neutralino]

In this thread I intend to present some of the observational evidence for, firstly, the expansion of the universe, and secondly why we think the universe is accelerating in its expansion today. I will make use of many of the references references that I posted in References and Sources of Info on Standard Cosmology and will try and reference things correctly.

I also invite questions and discussion, but please let's try and avoid religious and/or philosophical comments.

So, let's begin.

In the mid 1920's, Edwin Hubble [1] was observing a group that he called "spiral nebulae," but which we now know were distant sprial galaxies, at Mount Wilson Observatory. These galaxies contained a very special type of stars called Cepheid Variables. Cepheid variables are stars slightly larger than our sun which are growing old to become Red Giants; however they do this in a special way. Heat is trying to escape from the core but it builds up inside the star. This pushes the outer layers up, so the radius of the star increases by a small amount. With a greater surface area, this star now looks brighter. However, due to the fact that the surface area is now greater, it means that the star can radiate this extra heat energy off into space, which in turn allows the radius to return to normal, and so the star's brightness returns to normal. This is a cyclic process, and has period of a few days. In the early 1900's, Henrietta Swan Leavitt [2] had shown that the intrinsic brightness of a Cepheid Variable is related to the period of it's light output variation. So, if you find a Cepheid Variable with a period of, say, 10 days, then it will have the same intrinsic brightness as any other Cepheid Variable with a period of 10 days. If some appear to be dimmer than others, it means that they are further away. (See [3] for a more scientific explanation of Cepehid Variables)

Another thing we need to know is how to measure velocities of distant galaxies. This is done using redshift. See reference [4] for more information.

So, using Cepheid Variables as standard candles to measure distance, and using redshift to measure velocity of distant galaxies, Hubble published a claim [5] that the radial velocities of galaxies are proportional to their distances; i.e. [imath]\vec{v}=H\vec{r}[/imath], where [imath]\vec{v}[/imath] is the velocity of the galaxy, [imath]\vec{r}[/imath] is the displacement of the galaxy from the earth, and H is the so-called "Hubble constant" (which is a constant in space but not in time).

Here is the graph that he plotted (from [5]).


So, we can see that this figure confirms Hubble's claim of the proportional relationship between displacement and velocity. Now, one may think by looking at that graph that Hubble has just decided to draw a straight line through some points that look like there is some sort of relationship, but one that's not precisely linear: this was probably because Hubble knew what he was looking for! However, later work has shown that Hubble confused two different types of Cepheid Variables, and hence had a few errors in there. More recent supernovae data has confirmed Hubble's law in this range of redshifts more dramatically.



So, what does this all mean? Well, since Hubble has shown that, for a range of different galaxies, the velocity of recession is proportional to the distance, then we can say that every galaxy is moving away from us. Since we believe in the cosmological principle [6], we know that we cannot be in a special place in the universe, and so we can say that every galaxy is moving away from every other galaxy. This implies that the universe must be expanding.

Is this the end of the story? Is Hubble's law entirely correct? In my next post, we'll take a look at why we now think the universe is accelerating in its expansion.


[1] http://www.time.com/time/time100/sci...le/hubble.html
[2] http://en.wikipedia.org/wiki/Henrietta_Swan_Leavitt
[3] http://map.gsfc.nasa.gov/m_uni/uni_101expand.html
[4] http://www.astro.ucla.edu/~wright/doppler.htm
[5] http://antwrp.gsfc.nasa.gov/diamond_.../hub_1929.html
[6] http://csep10.phys.utk.edu/astr162/l...mology/cp.html

[Profpat]

Hi Neutralino;

Thanks for the informative post.
Will you also be addressing spatial inflation, or is Guth's theories a bit too theoritical for mainline physics?

Best,

Pat

[neutralino]

Hi Neutralino;

Thanks for the informative post.

You're welcome

Will you also be addressing spatial inflation, or is Guth's theories a bit too theoritical for mainline physics?

We can, indeed, talk about inflation. Inflation is generally accepted as part of the standard model anyway nowadays, since it irons out some of the problems of cosmology. I was planning on talking about the evidence for the acceleration of the universe at the present day first, but then I can go on to talk about inflation if you would like. (It may take a while to write; but we've got the whole month havn't we!) Feel free to add anything you feel may be relevant, Pat, and others.

[Profpat]

Thanks Neutralino;

Expansion I think I understand.( It makes sense )
Accelerating Expansion, is where I start to get confused ( It appears this is where it gets more theoritical , as to why the acceleration )
Inflation quite honestly blows my mind. ( This is where it seems they are trying to fill in a hole that they can't quite explain. Somewhat similar with coming up with 2 new forces to explain nuclear bonding. Also accepting the violation of symmetry to explain matter )

So any help you may give me and others regarding these, would be appreciated.

Best to you,

Pat

[neutralino]

Thanks Neutralino;

Expansion I think I understand.( It makes sense )
Accelerating Expansion, is where I start to get confused ( It appears this is where it gets more theoritical , as to why the acceleration )
Inflation quite honestly blows my mind. ( This is where it seems they are trying to fill in a hole that they can't quite explain. Somewhat similar with coming up with 2 new forces to explain nuclear bonding. Also accepting the violation of symmetry to explain matter )

So any help you may give me and others regarding these, would be appreciated.

Best to you,

Pat

Ok, well bear with me a few days, and I'll try and provide some information for you. Inflation's nice: it solves a lot of the problems that the big bang theory creates (I'll give a summary of those before we discuss inflation.)

[Profpat]

No rush Nuetralino;

In fact you should stay on track with the expansion.

But when time permits you may wish to address this subject for my and others education.

Thanks,

Pat

[MJA]

In this thread I intend to present some of the observational evidence for, firstly, the expansion of the universe, and secondly why we think the universe is accelerating in its expansion today.


So, what does this all mean? Well, since Hubble has shown that, for a range of different galaxies, the velocity of recession is proportional to the distance, then we can say that every galaxy is moving away from us. Since we believe in the cosmological principle [6], we know that we cannot be in a special place in the universe, and so we can say that every galaxy is moving away from every other galaxy. This implies that the universe must be expanding.

Hi N,

Thanks for the explanation that ultimately proved Einstein's cosmological constant incorrect.

I have always had great difficulty believing it though.

My main concern is the belief that because we measure a part or some of our universe as expanding, how is it that we can assume without knowledge of the extent of our yet infinite universe, that the universe is expanding in it's entirety?

Or a simply analogy would be: if the grass is green in my front yard, it does not necessarily mean that all grass is green everywhere in the infinite universe.

Or if one measures the motion of a river, it is truly moving in a single direction.
But it is also true that parts of the river are heading in infinite directions too.
So does a river move in a single or infinitely different directions?
If you test or measure a river by throwing a stick in it to see the direction of flow,
you will see its imeasurably infinite in all direction.

Is the universe expanding and contracting in places too?
What is the universe, should that be answered first?


=
MJA

[neutralino]

Hi N,

Thanks for the explanation that ultimately proved Einstein's cosmological constant incorrect.

You're welcome. However, as we'll see when I write my next part of the story, we'll put the cosmological constant back in!

I have always had great difficulty believing it though.

My main concern is the belief that because we measure a part or some of our universe as expanding, how is it that we can assume without knowledge of the extent of our yet infinite universe, that the universe is expanding in it's entirety?

I think this is a valid concern to have. However, as I said in my opening post, the reason we believe the whole of the universe to be expanding is due to the cosmological principle. There are various versions of this; one says that (on cosmological scales) no matter where we look in the universe we will see the same distribution of objects. There has been evidence which suggests that the cosmological principle is correct (CMB data, for example) and, besides, if the cosmological principle didn't hold, then we couldn't do cosmology!

[neutralino]

To recap: upto now we've learnt that Hubble, in the late mid 1920's discovered that the universe is expanding. As MJA correctly pointed out, this caused Einstein to discard the cosmological constant from his general theory of relativity, which he had originally introduced in order to produce a static solution to his theory. I'm sure everyone has heard that Einstein called this the "biggest blunder of his life," as he changed his theory to agree with the general consensus at the time rather than listen to the mathematics.

Hubble's law held until very recently, in fact around 1998, when the first news came that we had observations implying that the universe is actually accelerating in its expansion. As I briefly touched upon earlier, this new data came about from the observations of supernovae (technically, type Ia SNe). Supernovae are more effective standard candles than Cepheid variables simply because they are much brighter. Cepheid variables can be seen out to around 10-20 Mpc whereas type Ia Sne can be seen out to around 1000Mpc. This type of supernova is basically made up of a binary system of a small white dwarf and a massive star. The white dwarf accretes mass off the large star until it reaches some threshold and then the mass becomes too large that it implodes, causing the core to ignite: this creates an incredibly bright flash; a supernova. This type of SNe can be used as standard candles since every one reaches the same maximum luminosity.

Data collected from type Ia SNe is shown in the graph below. This particular set of data is from a paper written in 2003 [1] (Sorry the bottom axis should be labelled redshift, and the major increments are 0.01, 0.1, 1. This is obviously plotted on a logarithmic scale)



We can see from the diagram that, for small redshifts, we have the linear relationship that Hubble discovered. However, for larger redshifts, the relationship between distance and redshift deviates from a linear relationship. Now, it may not be obvious to the eye, but it can be shown using statistical tests, that this data is in fact evidence that the universe is accelerating in its expansion. You can see the three lines of "best fit" which basically are a fit to the data depending on the model of cosmology that you are using. The bottom line is for a universe completely containing matter, and the top universe is one which consists of 30% matter and 70% dark energy. Performing a statistical test on this data gives (assuming pressureless matter) a result of 1% probabilty that we live in a universe with no dark energy. That is, there is a 99% probability that we live in a universe that is accelerating in its expansion. (Recall that Dark Energy is simply a term used to describe the thing that is making the universe expand).

Finally, mathematical treatment shows that the standard model predicts a deviation from the linear relationship governed by the following equation (I promise this will be the only maths in this post!)
[math]D_L\approx\frac{c}{H_0}\left[z+\frac{1}{2}(1-q_0)z^2\right][/math]

Here D_L is the luminosity distance, measured from the properties we know about the standard candles. H_0 is the value of the Hubble constant at the current epoch, z is redshift, and q_0 is the "deceleration parameter" at the current epoch. The latter is a measure of the deceleration of the universe now, and so we expect it to be negative if the universe is indeed accelerating.

We can see, from the above formula that, at low redshifts, Hubble's law is obeyed; i.e a linear relationship between distance and recession velocity. However, at higher redshifts (*) we have a correction to the formula, and so the relationship is no longer linear. Thus, the prediction from the standard model, and the observational data from the type Ia SNe agree with each other.


(*)Note that, since z^2 appears in the second term, for small redshifts this would be negligible, and so the second term only contributes to higher redshifts.
[1] http://arxiv.org/abs/astro-ph/0303428


In my next post, I will go on to talk about inflation. If there are any questions, or points to discuss, feel free to post them.

[dleviwing]

Neutralino;
You seem to have skipped Pat’s question about Guth’s theory. Like many young novice scientist Guth treated BB theory as if it meant the universe started with an explosion. Guth makes for good reading though. Here is a link to add to your already fine collection.
http://www.users.globalnet.co.uk/~slocks/links/Guth's%20Grand%20Guess.htm