Recitation 9: Big Bang Cosmology I

A. It may seem that Hubble's law conflicts with the basic supposition of Friedman Robertson Walker cosmology that the universe is homogeneous and isotropic in space. For Hubble's law tells us that everything is rushing away uniformly from our particular galaxy. Does not that make our galaxy some sort of special center of galactic motion, different from every other galaxy? The following calculations show that the galactic motions of Hubble's law look the same from every galaxy.

Consider (0) our galaxy and galaxies (I) 1,000,000 and (II) 2,000,000, and (III) 3,000,000 and (IV) 4,000,000 light years distant from us, all in the same direction. Compute the velocities of recession of the galaxies (I)-(IV) from us.

Now imagine that you are an observer located on galaxy (I). Recompute the velocities of recession of the other galaxies. Find that Hubble's law still holds. That means that the expansion looks the same to an observer on galaxy 1 as it does from our galaxy. It is not hard to see that the same result will hold for all observers, no matter which galaxy is their home.

(In computing these velocities, use the ordinary Newtonian rule for composing velocities.)

B. The cosmic microwave background consists of radiation so feeble that we have to cool our instruments with liquid helium before we are able even to detect it. How much can we learn about the cosmos from a source so feeble?

C. If the universe turns out to have an open geometry so that space is infinite, then all of our observations are showing us only the tiniest part of space. It is a finite fragment of an infinite expanse. Given that tiny sample, are we justified in asserting that the universe is spatially homogeneous--the same in every place? Or is this fundamental hypothesis of cosmology mere supposition?