One of the things that cosmologists are not yet sure about is the Big Bang itself. It is not yet possible to give a definitive answer to the questions: what was the Big Bang and why did it happen? However, there has been a great deal of speculation recently on this subject, and it may not be long before a definitive, or almost definitive, answer will be declared. For the moment we will simply take the Big Bang as it is given, a huge explosion in which time and space began expanding. It is important to realize that space itself originated in the Big Bang. IT is tempting to think of the universe before the Big Bang as being a vast, infinite, expanse of empty space, like the space between the galaxy clusters today. The Big Bang, then, would have flung matter into this nothingness, but this is not what happened. Space itself was created during the Big Bang. Einstein and all subsequent cosmologists have viewed space as being as real as matter. In fact, physicists now view empty space as a sea of "virtual particles". So space is now expanding along with the galaxies and stars that exist with it and has been expanding ever since the Big Bang.
Actually, cosmologists actually have a clearer picture of what the universe was like during the period right after the Big Bang than they are about the universe today. The reason for this is universe was very simple, in comparison, then. The universe was filled with a hot soup of particles like a hot gas trapped in a box. The photons in the cosmic microwave background radiation are the last remnant of that hot soup. Everything else has evolved into more complex forms like planets, stars, and galaxies. From this background radiation, cosmologists have been able to learn things about the particles that filled the universe 18 billion years ago (the approximate time of the Big Bang).
Perhaps the single most important thing that we know about conditions immediately after the Big Bang is that the universe was extremely dense. That is, all the matter and energy in it was compressed very tightly together. On the other hand we do not know how big the universe was immediately after the Big Bang. Because we do not know how big the universe is now. If the Universe is infinitely large then it would have been infinitely large then, because there is now way something could go from have a finite size to having an infinite size. So if the universe has a finite size today then it had a finite, and proportionally small, size then.
We do, however, know how large the visible universe would have been immediately after the Big Bang. The visible universe is the portion of the universe that an observer, imaginary for comparison, would be able to see. The visible universe today has a radius of about 18 billion light years, because that is how far light has been able to travel in the approximately 18 billion years since the Big Bang. Anything outside of that 18 billion light year radius would be invisible to us because the light from it has not reached us yet. This would be true for observers anywhere in the universe, not just earth. Observer more than 18 billion years from earth would...