Hubble Diagram is probably the most 
traditional of cosmological test. 
It plots relative luminosity distance 
sources as a functional derived shift. 
In earlier on the brightest things that 
astronomers could think of to look at the 
brightest cluster galaxies, they can be 
detected out to [UNKNOWN] from using the 
technology available at that time, that 
there are not to be quite far enough to 
really sense cosmological effects. But 
moreover the problem was that galaxies 
had been made out of stars, evolve, 
because stars evolve. 
And, moreover, they merge, so their total 
stellar mass increases. 
And so by the 1980's, it became clear, 
that Hubble diagram for galaxies, is 
basically an impossible task. 
Because the evolutionary effects really 
dominate over any cosmological effect. 
The difference between different 
evolutionary models is much larger than 
between any plausible range of 
cosmological models. 
Supernovae were also suggested as 
standard candles, as early as the 1960's 
by [UNKNOWN] collaborators. 
But back then, nobody knew how to make 
them standard enough for this purpose. 
The revival of this test came in mid 
1990s, where astronomers learned how to 
standardize brightness of supernovae in 
the ways that we covered earlier in the 
class. 
And because they can be seen further away 
telescopes are bigger and detectors are 
better, suddenly they became a viable 
cosmological test again. 
Do note that some uncertainties still 
remain about the origin of, of supernova 
type 1a and exactly what happens in those 
explosions, but astronomers strive to 
come up with tests to control all 
possible systematics. 
We do see some variation for light curves 
but most of it can be then taken out 
through standardization procedures. 
The some remaining questions such as 
whether there is an additional parameter, 
there is an evolution and there are hints 
that indeed such things do happen, but at 
such a subtle level they do not affect 
the cosmological results. 
Still, keep in mind these are Messy 
stellar explosions which we can barely 
model in computers today. 
And the more realistic the models would 
get, the more complicated they look. 
So it's still possible that some 
additional uncertainties might be present 
using supernovae standard [UNKNOWN]. 
These are examples of images of some of 
the very distant super novae taken with 
Hubble space telescope. 
This is just to indicate how difficult 
these observations are. 
Not only do these faint supernovae have 
to be discovered, they have to be 
discovered early, their light curves 
mapped, their red shifts obtained, all of 
the different corrections applied, and 
only then they can be used in Hubble 
diagram. 
All of this requires a lot of effort by 
the best people and the best equipment 
that we have. 
Anyway, that was done in mid 90's, by 2 
groups working independently. 
One was the supernova cosmology project, 
at Lawrence Berkeley Lab, led by Saul 
Perlmutter, and the other one, was, High 
redshift Supernova Team, led by Brian 
Schmidt, and Adam Riess. 
The 2 groups, essentially produced the 
same result, at roughly the same time. 
And more or less, independent. 
They both found out, that the high 
redshift supernova Hubble diagram, 
requires introduction of the cosmological 
constant or vacuum energy density in 
order to fit the data. 
Whereas, there was a lot of 
circumstantial evidence for cosmological 
constant prior to that. 
This was the first time that majority of 
physicists really started paying 
attention and taking this possibility 
seriously. 
Here we see Hubble diagrams with the main 
trend line subtracted a particular model 
subtracted and then residuals fit for 
variety fodder models. 
The model that fits the data best, is the 
one that includes cosmological constant, 
at a level of approximately 70% of 
critical density. 
This was a spectacular result, and the 3 
leaders of the groups, deservedly got 
Nobel Prize, for that work. 
Although, again, it's important to point 
out, that These are large, team efforts, 
and not necessarily reducible to a 
handful of individuals. 
This is how science today operates. 
Here is the Hubble diagram replotted now 
in the original traditional sense of 
scale factor versus time. 
And so, the points extend to the past, 
you can see that they select a particular 
curve And that curve, corresponds to, 
cosmological constant, driven universe, 
that expands forever. 
Many other groups, have undertaken this 
work since then, and they all pretty much 
agree. 
The results just get better, and better. 
Here is an example of one of the more 
modern High redshift supernova Hubble 
diagrams, and colors of points correspond 
to those, from different groups. 
As you can see, there is an excellent 
mutual agreement, and the signal to noise 
is really getting to be very good. 
So this was the upshot, of the supernova 
Hubble diagram. 
On the plot of Critical dense, I'm, on 
the plot of, density parameters, matter 
on the x-axis and vacuum or cosmological 
constant on the y-axis. 
The measurements define an error ellipse, 
which is tilted and the plot universe 
corresponds to a diagonal straight line, 
as shown here. 
They do intersect and intersect roughly 
at density of matter of .3 for critical 
density and density vacuum about 0.7 for 
critical density. 
So this is the 1st time it was possible 
to say that if the universe was flat, 
then there must be a cosmological 
constant. 
But note that these error ellipses are 
pretty large and they do not really nail 
down the exact cosmological model. 
The zero value of cosmological constant 
is sufficiently far from the best fit 
that it can be excluded. 
But exactly what mixture of vacuum 
density and matter densities at play had 
to be determined using some other method. 
An interesting twist to this is to use 
cosmic gamma ray bursts as alternative 
standard candles, these are even more 
spectacular explosions. 
But it turns out, that their gamma 
variable luminosity can be also 
standardized to a nearly constant value 
using a variety of other parameters. 
At any rate, it's an independent test on 
what supernova results are and here are 
the error contours from gamma ray bursts 
alone. 
There are bigger than those from 
supernovae because gamery versus not 
quite a good standard candle but they 
produce more or less the same result. 
Now few words about the other classical 
cosmological test, the angular diameter 
test. 
Here we compare relative angular diameter 
distances to source as the different 
[UNKNOWN], and in the past things like 
isophotal sizes of giant elliptical 
galaxies, mean seperation of galaxies in 
clusters, or seperation of radio lobes in 
radio sources, we're all suggested that 
as standard rulers. 
And non of them really is for the same 
reasons as before evolution. 
Here is some of the earlier results 
trying to do that and interestingly 
enough all of these have also in 
consistent in what we now know is the 
correct cosmology. 
But People simply could not be sure, 
because of the evolutionary effect that 
was not well understood at the time. 
This test got revived through the cosmic 
microwave background. 
And it's probably now the most important 
of all of our tools. 
So next time we will talk about cosmology 
Cosmic microwave background fluctuations. 
What really led us into the era of 
precision cosmology.