Notes on Relativity and Cosmology - Physics Department, UCSB

284 CHAPTER 10. COSMOLOGY
Well, the stars are not in fact evenly sprinkled. We now know that they are
clumped together in galaxies. And even the galaxies are clumped together a
bit. However, if one takes a sufficiently rough average then it is basically true
that the clusters of galaxies are evenly distributed. We say that the universe
is homogeneous. Homogeneous is just a technical word which means that every
place in the universe is the same.
10.1.1 Homogeneity and Isotropy
In fact, there is another idea that goes along with every place being essentially
the same. This is the idea that the universe is the same in every direction. The
technical word is that the universe is isotropic. To give you an idea of what this
means, I have drawn below a picture of a universe that is homogeneous but is
not isotropic – the galaxies are farther apart in the vertical direction than in
the horizontal direction:
In contrast, a universe that is both homogeneous and isotropic must look roughly
like this:
10.1.2 That technical point about Newtonian Gravity in
Homogeneous Space
By the way, we can use the picture above to point out that technical problem
I mentioned with Newtonian Gravity in infinite space. I will probably skip this
part in class, but it is here for your edification.
The point is that, to compute the gravitational field at some point in space we
need to add up the contributions from all of the infinitely many galaxies. This
is an infinite sum. When you discussed such things in your calculus class, you