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.