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Another approach to studying the history 
of our universe, the, measuring the 

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cosmological parameters is to do what we 
discussed at the beginning. 

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You can try to measure the deviations 
from the linear red shift. 

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Distance relation that is the Hubble law, 
and remember the deviations are sensitive 

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to the history of the universe, and so 
how would you do that? Well, you can 

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measure the red shift of some object. 
You need to measure the distance to the 

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same object. 
How do you measure the distance of 

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things? we're good at that by now. 
To measure the distance to something, you 

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need to know its luminosity, 
measure its brightness and use the equals 

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all over pi d squared. You have to 
remember to use luminosity distance, 

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corrective for redshift, but you're 
measuring the redshift. 

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What you need is a object you can see at 
great distance, which therefore has to be 

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very luminous, and whose luminosity you 
know, 

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we made a big deal about such objects, 
type 1A Supernovae. 

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The explosions of white dwarves as they 
approach the Chandrasekhar limit, because 

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of accretion from a binary partner, form 
precisely, very luminous standard 

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candles. 
And so, at the early years of this 

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century and the last years of the last, 
two groups set out to use type 1A 

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supernovae as standard candles, measure 
their brightness, know their luminosity, 

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compute the luminosity distance, measure 
the redshift of their absorption line of 

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silicon and so on, and figure out the 
redshift, and figure our the corrections 

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to the Hubble Law at large redshifts. 
what does this mean? Well, what they were 

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looking for is a measurement of the 
deceleration parameter. 

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Remember, 
we expect expansion to be slowed down by 

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gravitation attraction, and so we expect 
that in the past, expansion was more 

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rapid than it is now. 
Convert that to what you expect for the 

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redshift, you expect the redshift of 
distant galaxies to be larger than 

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predicted by the Hubble Law. We saw that 
for the positive curvature of universe, 

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in my dust universe model, when I, we, 
played around with those examples. And so 

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here is the data from which they can 
learn this. You see that the data is 

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quite noisy, you see that they have made 
amazing achievements. They have measured 

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Type 1A supernovae up to z equals 1. 
That's a distance of about 13.8 billion 

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light years away. That's a large 
distance. 

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and while the data is noisy, they managed 
to draw a conclusion, and both groups 

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drew the same conclusion. 
And the surprising conclusion was, that 

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the deceleration parameter is negative. 
In other words, we live in an era in 

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which expansion is accelerating, which 
means that since all kinds, both dust and 

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radiation, all kinds of normal matter, 
contribute to deceleration, the only 

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expression in our equations that drive 
acceleration is the cosmological term 

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with its weird negative pressure, and for 
that reason, we think that this is a 

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almost direct measurement of the presence 
of a cosmological term. 

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You notice here that the deviations they 
are measuring from the Hubble Law, and 

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the distinction they can make based on 
this data requires some analyses. 

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But if you assume that there is no vacuum 
energy, this would be your predicted 

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Hubble relation corrections, 
and clearly this is excluded from what 

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they have measured. 
And so they actually have a precise 

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measurement. 
here's a historical view putting the 

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supernovae at the time at which they 
actually exploded, and this is the The 

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selected pattern of expansion that we are 
seeing, and you see that, what we're, 

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what they are measuring, is sort od this 
very slight positive curvature over here, 

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as we said, we are in the process of 
turning over from slowing matter 

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dominated it's Or dust dominated 
expansion like to 2^2/3 into an 

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exponential. 
We're in the transition region today and 

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we are measuring this slight bit of 
positive curvature. 

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So another constraint on cosmological 
parameters, and between that and the 

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previous one let's see what we have.