Actually, it should be noted that while Stephen Hawking was a big supporter of the big bang theory in the 70's, he has changed his mind in more recent times. The idea of the big bang basically came from Einstein's thoery of general relativity, which predicted that due to the current expansion of the universe and our observations of the past, the universe must have been born from a singularity in which matter was infinitely dense and time was infinately slow (basically an infinite warp in the fabric of space-time). In his book, A Brief History of Time (revised 1998), he points out a few features of the big bang that simply don't add up.
  • If the universe began as a singularity, why was it so hot? (as evidenced by cosmic background radiation)
  • Why is the universe uniform on a macroscopic scale? Most notably, radiation is very nearly the same from every direction is space indicating that heat is coming to us from all directions equally rather than one direction as one would expect from a singularity.
  • Why did the universe start expanding at a critical rate that would allow it to continue to be expanding at nearly the same critical rate today?
  • What is the origin of the density fluctuations that must have existed in order to form clumps of matter in galaxies surrounded by empty space? An exploding infinitely small, infinitely dense singularity should be very uniform in how it distributes matter.

Hawking investigated the quantum effects of the past and believes that the universe never began nor will it end, it just is. That is to say, space-time has no boundaries, yet it is still finite. This is pretty hard to grasp because we cannot really comprehend this a 4 dimensional world. The example Hawking uses is that it's like the earth, which in two dimensions has no boundaries (you can go around and around without reaching a boundary) but it does have a finite size. The tricky part is extrapolating this concept to 4 dimensions instead of 2 :)