If at the time of the big bang, if the expansion rate was more than the speed of light, will we know? after all the visible universe ends at about 10-20 billion light years or so (or so I read), but can't it just be the end of our horizon, as the expansion was greater than light speed before that period?
That's a really good (and hard) question. When you read about cosmology, you might have read about the cosmic microwave background (CMB). Before the CMB originated, the universe was opaque to light. So, we can never see beyond the CMB, and due to this, we can never see to the instant of the Big Bang. Consequently, there is no direct way of telling whether the expansion was at sometime faster than the speed of light. But there are several indirect pieces of evidence which can tell you about the early universe.
But first, let me tell you as to what would happen if at some instant, the universe did expand faster than the speed of light. In this case, as you have pointed out, the horizon distance will be the point at which the expansion was just at the speed of light; what you have called as the "end of our horizon".
So, if the universe never expanded faster than the speed of light, then we could see to the Big Bang, were it not for the CMB which blocks off light before that epoch. But, if at some point it DID expand faster than the speed of light, we will see to the "end of our horizon".
There are a few problems with standard Big Bang cosmology, which can be solved by "inflation" (an exponential expansion of the universe, which will be faster than the speed of light). The problems with standard cosmology are (a) the flatness problem (b) the horizon problem and (c) the origin of density fluctuations (which grew to galaxies and stars today).
They are a little bit technical, and you can look at books to see a qualitative explanation about these problems. If you are interested in knowing more, then write back, and I can elaborate. Inflationary cosmology solves these problems in the following way: in the early phase of the universe, it went through a phase called inflation, during which period, the universe expanded by a factor of more than 1050 in a time-scale of less than 10-30 seconds. So, there is some evidence that the universe DID undergo a period of expansion faster than the speed of light. But as you can see, the evidence is quite indirect and not something that we can directly see.
This page was last updated June 27, 2015.