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Hubble Diagram is probably the most 
traditional of cosmological test. 

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It plots relative luminosity distance 
sources as a functional derived shift. 

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In earlier on the brightest things that 
astronomers could think of to look at the 

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brightest cluster galaxies, they can be 
detected out to [UNKNOWN] from using the 

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technology available at that time, that 
there are not to be quite far enough to 

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really sense cosmological effects. But 
moreover the problem was that galaxies 

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had been made out of stars, evolve, 
because stars evolve. 

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And, moreover, they merge, so their total 
stellar mass increases. 

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And so by the 1980's, it became clear, 
that Hubble diagram for galaxies, is 

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basically an impossible task. 
Because the evolutionary effects really 

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dominate over any cosmological effect. 
The difference between different 

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evolutionary models is much larger than 
between any plausible range of 

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cosmological models. 
Supernovae were also suggested as 

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standard candles, as early as the 1960's 
by [UNKNOWN] collaborators. 

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But back then, nobody knew how to make 
them standard enough for this purpose. 

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The revival of this test came in mid 
1990s, where astronomers learned how to 

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standardize brightness of supernovae in 
the ways that we covered earlier in the 

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class. 
And because they can be seen further away 

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telescopes are bigger and detectors are 
better, suddenly they became a viable 

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cosmological test again. 
Do note that some uncertainties still 

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remain about the origin of, of supernova 
type 1a and exactly what happens in those 

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explosions, but astronomers strive to 
come up with tests to control all 

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possible systematics. 
We do see some variation for light curves 

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but most of it can be then taken out 
through standardization procedures. 

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The some remaining questions such as 
whether there is an additional parameter, 

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there is an evolution and there are hints 
that indeed such things do happen, but at 

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such a subtle level they do not affect 
the cosmological results. 

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Still, keep in mind these are Messy 
stellar explosions which we can barely 

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model in computers today. 
And the more realistic the models would 

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get, the more complicated they look. 
So it's still possible that some 

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additional uncertainties might be present 
using supernovae standard [UNKNOWN]. 

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These are examples of images of some of 
the very distant super novae taken with 

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Hubble space telescope. 
This is just to indicate how difficult 

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these observations are. 
Not only do these faint supernovae have 

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to be discovered, they have to be 
discovered early, their light curves 

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mapped, their red shifts obtained, all of 
the different corrections applied, and 

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only then they can be used in Hubble 
diagram. 

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All of this requires a lot of effort by 
the best people and the best equipment 

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that we have. 
Anyway, that was done in mid 90's, by 2 

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groups working independently. 
One was the supernova cosmology project, 

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at Lawrence Berkeley Lab, led by Saul 
Perlmutter, and the other one, was, High 

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redshift Supernova Team, led by Brian 
Schmidt, and Adam Riess. 

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The 2 groups, essentially produced the 
same result, at roughly the same time. 

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And more or less, independent. 
They both found out, that the high 

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redshift supernova Hubble diagram, 
requires introduction of the cosmological 

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constant or vacuum energy density in 
order to fit the data. 

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Whereas, there was a lot of 
circumstantial evidence for cosmological 

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constant prior to that. 
This was the first time that majority of 

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physicists really started paying 
attention and taking this possibility 

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seriously. 
Here we see Hubble diagrams with the main 

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trend line subtracted a particular model 
subtracted and then residuals fit for 

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variety fodder models. 
The model that fits the data best, is the 

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one that includes cosmological constant, 
at a level of approximately 70% of 

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critical density. 
This was a spectacular result, and the 3 

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leaders of the groups, deservedly got 
Nobel Prize, for that work. 

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Although, again, it's important to point 
out, that These are large, team efforts, 

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and not necessarily reducible to a 
handful of individuals. 

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This is how science today operates. 
Here is the Hubble diagram replotted now 

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in the original traditional sense of 
scale factor versus time. 

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And so, the points extend to the past, 
you can see that they select a particular 

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curve And that curve, corresponds to, 
cosmological constant, driven universe, 

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that expands forever. 
Many other groups, have undertaken this 

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work since then, and they all pretty much 
agree. 

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The results just get better, and better. 
Here is an example of one of the more 

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modern High redshift supernova Hubble 
diagrams, and colors of points correspond 

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to those, from different groups. 
As you can see, there is an excellent 

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mutual agreement, and the signal to noise 
is really getting to be very good. 

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So this was the upshot, of the supernova 
Hubble diagram. 

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On the plot of Critical dense, I'm, on 
the plot of, density parameters, matter 

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on the x-axis and vacuum or cosmological 
constant on the y-axis. 

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The measurements define an error ellipse, 
which is tilted and the plot universe 

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corresponds to a diagonal straight line, 
as shown here. 

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They do intersect and intersect roughly 
at density of matter of .3 for critical 

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density and density vacuum about 0.7 for 
critical density. 

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So this is the 1st time it was possible 
to say that if the universe was flat, 

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then there must be a cosmological 
constant. 

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But note that these error ellipses are 
pretty large and they do not really nail 

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down the exact cosmological model. 
The zero value of cosmological constant 

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is sufficiently far from the best fit 
that it can be excluded. 

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But exactly what mixture of vacuum 
density and matter densities at play had 

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to be determined using some other method. 
An interesting twist to this is to use 

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cosmic gamma ray bursts as alternative 
standard candles, these are even more 

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spectacular explosions. 
But it turns out, that their gamma 

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variable luminosity can be also 
standardized to a nearly constant value 

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using a variety of other parameters. 
At any rate, it's an independent test on 

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what supernova results are and here are 
the error contours from gamma ray bursts 

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alone. 
There are bigger than those from 

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supernovae because gamery versus not 
quite a good standard candle but they 

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produce more or less the same result. 
Now few words about the other classical 

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cosmological test, the angular diameter 
test. 

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Here we compare relative angular diameter 
distances to source as the different 

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[UNKNOWN], and in the past things like 
isophotal sizes of giant elliptical 

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galaxies, mean seperation of galaxies in 
clusters, or seperation of radio lobes in 

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radio sources, we're all suggested that 
as standard rulers. 

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And non of them really is for the same 
reasons as before evolution. 

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Here is some of the earlier results 
trying to do that and interestingly 

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enough all of these have also in 
consistent in what we now know is the 

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correct cosmology. 
But People simply could not be sure, 

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because of the evolutionary effect that 
was not well understood at the time. 

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This test got revived through the cosmic 
microwave background. 

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And it's probably now the most important 
of all of our tools. 

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So next time we will talk about cosmology 
Cosmic microwave background fluctuations. 

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What really led us into the era of 
precision cosmology.