Another approach to studying the history 
of our universe, the, measuring the 
cosmological parameters is to do what we 
discussed at the beginning. 
You can try to measure the deviations 
from the linear red shift. 
Distance relation that is the Hubble law, 
and remember the deviations are sensitive 
to the history of the universe, and so 
how would you do that? Well, you can 
measure the red shift of some object. 
You need to measure the distance to the 
same object. 
How do you measure the distance of 
things? we're good at that by now. 
To measure the distance to something, you 
need to know its luminosity, 
measure its brightness and use the equals 
all over pi d squared. You have to 
remember to use luminosity distance, 
corrective for redshift, but you're 
measuring the redshift. 
What you need is a object you can see at 
great distance, which therefore has to be 
very luminous, and whose luminosity you 
know, 
we made a big deal about such objects, 
type 1A Supernovae. 
The explosions of white dwarves as they 
approach the Chandrasekhar limit, because 
of accretion from a binary partner, form 
precisely, very luminous standard 
candles. 
And so, at the early years of this 
century and the last years of the last, 
two groups set out to use type 1A 
supernovae as standard candles, measure 
their brightness, know their luminosity, 
compute the luminosity distance, measure 
the redshift of their absorption line of 
silicon and so on, and figure out the 
redshift, and figure our the corrections 
to the Hubble Law at large redshifts. 
what does this mean? Well, what they were 
looking for is a measurement of the 
deceleration parameter. 
Remember, 
we expect expansion to be slowed down by 
gravitation attraction, and so we expect 
that in the past, expansion was more 
rapid than it is now. 
Convert that to what you expect for the 
redshift, you expect the redshift of 
distant galaxies to be larger than 
predicted by the Hubble Law. We saw that 
for the positive curvature of universe, 
in my dust universe model, when I, we, 
played around with those examples. And so 
here is the data from which they can 
learn this. You see that the data is 
quite noisy, you see that they have made 
amazing achievements. They have measured 
Type 1A supernovae up to z equals 1. 
That's a distance of about 13.8 billion 
light years away. That's a large 
distance. 
and while the data is noisy, they managed 
to draw a conclusion, and both groups 
drew the same conclusion. 
And the surprising conclusion was, that 
the deceleration parameter is negative. 
In other words, we live in an era in 
which expansion is accelerating, which 
means that since all kinds, both dust and 
radiation, all kinds of normal matter, 
contribute to deceleration, the only 
expression in our equations that drive 
acceleration is the cosmological term 
with its weird negative pressure, and for 
that reason, we think that this is a 
almost direct measurement of the presence 
of a cosmological term. 
You notice here that the deviations they 
are measuring from the Hubble Law, and 
the distinction they can make based on 
this data requires some analyses. 
But if you assume that there is no vacuum 
energy, this would be your predicted 
Hubble relation corrections, 
and clearly this is excluded from what 
they have measured. 
And so they actually have a precise 
measurement. 
here's a historical view putting the 
supernovae at the time at which they 
actually exploded, and this is the The 
selected pattern of expansion that we are 
seeing, and you see that, what we're, 
what they are measuring, is sort od this 
very slight positive curvature over here, 
as we said, we are in the process of 
turning over from slowing matter 
dominated it's Or dust dominated 
expansion like to 2^2/3 into an 
exponential. 
We're in the transition region today and 
we are measuring this slight bit of 
positive curvature. 
So another constraint on cosmological 
parameters, and between that and the 
previous one let's see what we have.