Distances at the decoupling epoch of the universe

[bojibridge]

Homework Statement

The photosphere of the universe corresponding to the age of decoupling of matter from radiation is presently 1.4 x 10^10 pc away from us. Calculate how far away a point on the photosphere was when the background radiation we see today was emitted.

Also, dark matter particles are thought to have decoupled from the rest of matter after inflation, around 10^-32 s. Repeat the first part for these particles, assuming same photosphere distance.

Homework Equations

Not really sure

The Attempt at a Solution

I know that the time at which the decoupling epoch occurred was approximately 10^5 years after the big bang. I don't think the question is supposed to be too complicated (ie taking into account uber astrophysics, you know.)

 

[Dick]

You have to put more information into this than you are telling us. Radiation decoupling marks the point when the photon background couldn't ionize hydrogen anymore. By some coincidence this is also the time that the universe shifted from a radiation dominated power law expansion to a matter dominated one. Can you give enough facts about the current universe to estimate the red shift at this time? When did the energy density represented by the CMB become comparable to the mass density? Then you have to use that to extrapolate (using a radiation dominated expansion law) back to 10^(-32) seconds and get the red shift factor then. This is reasonable astrophysics stuff, no heavy general relativity lifting required.