[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!)


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.