The problems of big bang theory. What are they?

A total understanding of the early universe is difficult. It requires a theory that can fully understand the very small and highly energetic as well as the very large. Quantum physics gives us insight into the small, relativity the very large. Marrying the two is a work in progress.The earliest conceptions of the big bang model fell apart hopelessly at the very small because of relativity's inadequacy at dealing with that level. We'd get lots of infinite values that made no sense.More recent models have tried to come to an understanding of the very small end of the big bang and attempted to create a complete chronology - with some good successes, but the main problems now relate to the point at which quantum processes are overwhelmed by relativistic considerations.A complex problem really - but one which can be relayed in simple terms.Other issues with early big bang include the dark energy issue and the cosmological constant. Things like this had to be assumed. Newer models make predictions about these figures (predictions which are reflected in reality), but there are more esoteric properties (I'm no expert, but I believe the shape of Calabi-Yau space might be one of these) which have to be assumed...hypotheses abound to explain some of these properties - but I don't think there is any finality on the issue at this point.

Good idea. Hard to do in practice, because individuals rarely get the chance to dictate phrases - once they get out there, they're difficult to control. Having seen this, I think there is more caution in naming things these days - but it isn't perfect. As humans we like certain phrases, even if they aren't accurate. We have a penchant for metaphor that is always going to be problematic.The big bang can be seen as a set of cosmological theories. Some of the later names are less contentious. How do you prefer "Inflationary Cosmology" for example? What's right about it? Beats me, but a lot of thought has gone into philosophy and science and about how and when we can make confident statements about the way the universe works. One of the principle ideas that has stuck is parsimony - and God just adds replaces one unexplained/unexplainable problem with another.