We now turn to Measurement of 
Cosmological Parameters. 
The first one of which, is Hubble 
Constant, or Hubble Parameter. 
It sets, both the spatial and temporal 
scales for the whole universe. 
In a given cosmological model, specified 
by values of different, omegas, or little 
w as well. 
All distances and all times scale 
linearly with Hubble's constant. 
And thus, its importance. 
So, the inverse of the Hubble constant is 
the characteristic time unit of 
cosmology. 
The Hubble time. 
Multiplied by the speed of light, it 
gives Hubble length. 
Which is commensurate with the size of 
the observable universe. 
Note that, Hubble's constant, is 
independent of all other cosmological 
parameters. 
We have this neat separation, between 
Hubble constant that sets the scale, and 
all under parameters that Describe the 
qualitative behavior of the universe. 
So distances to anything, galaxies, 
quasars, anything cosmology. 
Scale with Humboldt's constant and it's 
importance. 
Moreover. 
Physical parameters of, objects like 
galaxies or anything else, such as their 
total luminosity, or their masses or 
physical sizes, all scale, with the 
distance, with the appropriate power. 
And in order to understand these objects 
better, and how they form, how they 
evolve, we need, distances to them. 
However, measuring the distances in 
cosmology is, a very difficult thing to 
do. 
Because galaxies are very far away. 
And, in fact, the only distances in 
astronomy that are measured cleanly, 
without recourse 20 models or statistics, 
are trigonometric paralexes to stars. 
Everything else requires some sort of 
physical modeling or assumptions or 
statistics. 
Because we have a concept of the distance 
ladder. 
Which means, that we first measure, 
distances to objects that, where we're 
sure how to do it, such as nearby stars. 
Then we use that, to calibrate distances 
to some objects further away, star 
clusters say, and, so on and so on. 
So we calibrate the distance indicators 
relevant to each other. 
And this is what's known as the distance 
ladder. 
Locally, those will be various stellar 
types of indicators, say, based on 
pulsating stars or star clusters and 
things like that, then properties of 
nearby galaxies, using their scaling 
relations And sun, until we reach what is 
called pure Hubble flow, where only the 
recession of velocities matter. 
And that is where the expansion of the 
universe, unperturbed by local 
non-infirmities really sets in. 
Now the age of the universe, can be 
actually estimated Independent of 
Hubble's constant.The look back times, 
objects cannot, but the total age of the 
universe can. 
We can, for example, estimate ages of 
stars or clusters, or chemical elements 
and that gives a lower limit to the age 
of the universe. 
Independent of any measurements or 
distances. 
This is a hard thing to do, and thus, 
measurements of Hubble constant have 
somewhat disreputable history. 
Hubble's own estimate of it was an order 
of magnitude off from what we know today 
is more or less the correct value. 
And through the history, people always 
thought they knew it to about 10% 
accuracy. 
Even though its value changed by a whole 
order of magnitude. 
The reason for this is that they didn't 
really account properly for errors of 
measurement. 
And especially for the systematic errors. 
So, for example, when Hubble first 
measured value of Hubble's Constant. 
One over that was a couple billion years, 
and already then people knew that there 
were rocks on planet Earth that are three 
or four billion years old. 
So planet Earth was older than the 
universe, and that was a problem. 
Ever since then, the value of the Hubble 
constant was revised, usually downward. 
The first major revision was due to 
Walter Baddey who recognized that there 
are really two very different kinds of 
pulsating stars, one of which is confused 
for the other, and he came up with the 
concept of stellar populations. 
That immediately halved the value of 
Hubble's constant. 
Then improved measurements. 
Pushed it further down, and down. 
And in 1970's, it go down to the range 
of, between roughly 50 and 100 kilometers 
per second, per mega-parsec. 
There were two prominent schools of 
thought on this. 
One, led by Allen Sandage, the. 
The disciple of Hubble, pushed for the 
lower values, around 50 kilometers per 
second per megaparsec. 
The other one, led by Gerard de 
Vaucouleurs and his collaborators in 
Texas and elsewhere, pushed for twice 
that much, about 100 kilometers per 
second per megaparsec. 
And the 2 just could not just get into an 
agreement. 
The reasons for this were the. 
They made different assumptions, they 
used different calibrations, and things 
went like that until 1980's. 
But even in the modern days, the spread 
continued. 
People started being more careful about 
the error bars, and yet still the actual 
spread of quoted values in the literature 
was always larger error bars. 
That persisted until roughly, 1990's. 
There are two kinds of methods to measure 
distances. 
There are methods that obstensibly give 
absolute distances to particular kind of 
objects, like trigonometric parallax for 
stars, or using physical models to derive 
distances to supernovae or clusters of 
galaxies Galaxies. 
Parallax is the only safe one. 
The geometry is well-understood, and 
there are no problems. 
However, we cannot measure parallaxes of 
stars more than about kiloparsec from us 
now, well within sight of our own galaxy. 
There is so-called moving cluster method, 
but that relies on statistics and certain 
assumptions. 
There is so-called Baade-Wesselink method 
that uses pulsating stars. 
That too makes assumptions about stellar 
atmospheres and thing, things like that. 
A very simliar to it, is so called 
expanding photosphere method for 
supernova. 
They are one also has to make some, 
non-trivial assumptions, about physics, 
of what's really an exploding star. 
Pushing further into Hubble flow, there 
are 2 important methods. 
One is based on so called 
Sunyaev-Zeldovich effect, which measures 
Distances to clusters of galaxies using 
observations of cosmic microbackground. 
And of the x ray mission from clusters. 
We will talk about those in more detail. 
And the other one is using gravitational 
lens time delays. 
We will also address that one in due 
time. 
The other kind of distance indicators is 
the secondary ones. 
Which require callibration from somewhere 
else. 
They can be used to measure relative 
distances say things there are objects 
which may be further away but there zero 
point has to be obtained from something 
else. 
And there are many of those, both using 
stars and galaxies and we will address 
them all. 
So here is schematically what the 
distance ladder is like Each method, 
operates in certain range of possible, 
plausible distances. 
And hopefully it overlaps in part, at 
least, with another method, which then 
can reach deeper, and so on. 
That is what we call the distance ladder. 
Nearest to us, trigonometric parallaxes, 
can be used to measure distances. 
Proper motions of stars, can also be 
used. 
Looking at statistical sense. 
Then we can measure distances to some of 
the nearby star clusters. 
And use properties of star clusters to 
measure distances to even more distant 
ones. 
In particular, this leads to measurement 
to distances to pulsating stars. 
Cephids and so called RR-Lyrae Stars, 
which are key step in the measurements of 
the Hubble Constant. 
But notice that several steps precede. 
With those, we can measure distances to a 
number of nearby galaxies. 
And then we can calibrate distance 
indicator relations for galaxies 
themselves. 
Those are correlations between 2 
quantities. 
One of which does not depend on distance. 
Say, rotational speed of a galaxy. 
And the other one of which does, like 
luminosity. 
So these important distance relations can 
be used to measure distances to galaxies 
far away, but they have to be calibrated 
locally, with something else. 
Then super novae come in, and those are 
currently favorite ways of measuring 
distances in cosmology. 
From near to far. 
We will cover them in some detail. 
Once we go beyond the regime where it's 
easy to do galaxy distance indicators, 
two other methods come in, on really 
cosmological scales. 
The Sunyaev–Zel'dovich effect, and the 
Gravitational Lensing. 
In principle, they do not depend on the 
distance ladder, however they are 
model-dependent. 
And therefore, previous calibrations are 
important as a check. 
So, here is a schematic flow chart. 
It's not there to confuse you, it's just 
to show you, a little bit, how complex 
the network of measurments has to be, 
with mutual checks to find out how far 
things are in the universe. 
It starts. 
With nearer stars and goes all the way to 
supernovean and cosmological, truely 
cosmological scale. 
Well that's it for now, next time we will 
actually talk about stellar distance 
indicators.