1. The problem statement, all variables and given/known data Estimate the radius of the last scattering surface, using the age of the Universe. Why might this underestimate the true value? 2. Relevant equations For a matter dominated universe particle horizon distance = 3ct 3. The attempt at a solution I assumed the way to do this would be to get an estimate by putting the age of the universe into the particle horizon distance, but I thought this would give an overestimate as decoupling occurred 400000 years after the big bang and thus the light has been travelling for less time. Using the equation and the age of the universe to be 13.5 billion years I get a value of 12000Mpc. The Liddle book tells me the radius is 6000hMpc-1, and I don't think h is anywhere near 0.5. Dont know where i've gone wrong, this clearly does not underestimate....is there a better way of doing this problem?