I have heard in multiple locations that in the case of a flat universe, the universe is infinite. This seems to present multiple issues:
a) If a flat universe were infinite, would would the space of the Big Bang then not be infinite?
b) If the above is not the case, that seems to suggest that the geometry of the universe can evolve over time?
c) If the space of the Big Bang was infinite, and since space, time, matter, and energy came from the Big Bang, wouldn't the density of the universe at the start of the universe be equal to that of the universe now?
d) If the above is true, why are we told that the universe began in a very dense state? And also, if the universe indeed was more dense initially, would this not suggest that space must not be flat?
Note: Some of these questions depend on the answer to previous questions.