Recently I have watched videos on how the inflation theory solves some problems that arise from the Big Bang Theory. In particular, I have a few questions regarding the flatness problem and how the inflation theory manages to resolve it. But first I would like to explain my understanding of the flatness problem.
The flatness problem occurs where the current universe has a density so very close to the critical density, but that is weird because that would require the universe to have omega almost = 1 from the VERY beginning (and this probability is extremely small). It is said that if omega 'much' smaller/bigger than 1, then it would drive the universe to expand/contract exponentially.
How is this process of exponentially expansion/contraction different from the evolution of closed/open universe? Does inflation theory straight-up rejects any possibility of open/closed universe (which have omega more/less than 1)?
How is inflation different from expansion? In the sense that if there was no inflation but only expansion, then the density would deviate from critical density exponentially, but somehow if there was inflation, then the inflation would drive whatever initial density towards critical density, why's that?
I would really appreciate any clarification on this matter!