I realise this may be a really obvious question, but wikipedia and google haven't help settle my curiousity. If the universe is in fact a flat universe, as I believe has been proven with experimentation, this, if I am not mistaken, means the universe will continue to expand to a limit without ever reaching this limit, continously expanding slower and slower. However, according to many books I've read, by studying the Doppler effect and the Hubble redshift, cosmologists have calculated that the rate of expansion in the universe is in fact speeding up, and the end result will be masses of dark space between stars in the distant future. To me, these two seem to contradict each other, and my impression of what happened during the big bang. If the universe will never reach it's limit according to flat universe theory, then surely it has been forever slowing down since the big bang. However, if the universe is speeding up in it's expansion, it would suggest that at one point it will slow down, but where did this acceleration come from post-big bang? If stars, galaxies and planets are moving further apart at a greater speed than before, then surely the universe as a whole is expanding faster. Maybe I have mis-interpretated what the books have said, or made another basic mistake in my thinking, but I'd really appreciate someone putting my mind to rest on this one. Thanks a lot.