They are as follows...
Problems with the Big Bang
The hot big bang theory has been extremely successful in correlating the observable properties of our Universe. However, there are some difficulties associated with the big bang theory. These difficulties are not so much errors as they are assumptions that are necessary but that do not have a fundamental justification. The required discussion is technical, so we will be content with a rather superficial statement of the three basic problems that are associated with the big bang and how they might be cured by a new idea that arises from considering the implications of elementary particle physics for cosmology.
The Horizon Problem
We have already encountered the horizon problem in conjunction with the discussion of the cosmic microwave background: when we look at the microwave background radiation coming from widely separated parts of the sky, it can be shown that these regions are too separated to have been able to have ever communicated with each other even with signals travelling at light velocity. Thus, how did they know to have almost exactly the same temperature? This general problem is called the horizon problem, because the inability to have received a signal from some distant source because of the finite speed of light is termed a horizon in cosmology. Thus, in the standard big bang theory we must simply assume the required level of uniformity.
The Flatness Problem
The experimental evidence is that the present Universe has very low geometrical curvature in its spacetime (it is nearly flat). Theoretical arguments that are well established but too complex to go into here suggest that this is a very unlikely result of the evolution of the Universe from the big bang, unless the initial curvature is confined to an incredibly narrow range of possibilities. While this is not impossible, it does not seem very natural.
The Monopole Problem
The only plausible theory in elementary particle physics for how nuclei in the present universe were created in the big bang requires the use of what are called Grand Unified Theories (GUTs). In these theories, at very high temperatures such as those found in the instants after the Universe was created the strong, weak, and electromagnetic forces were (contrary to the situation today) indistinguishable from each other. We say that they were unified into a single force. Although there is as yet no certain evidence for the validity of such theories, there is strong theoretical reason to believe that they will eventually turn out to be essentially correct. Our current understanding of elementary particle physics indicates that such theories should produce very massive particles called magnetic monopoles, and that there should be many such monopoles in the Universe today. However, no one has ever found such a particle. So the final problem is: where are the monopoles?
http://csep10.phys.utk.edu/astr162/lect/cosmology/bbproblems.html
Thanks for the great post. For all the believers in God, and I am one, every discovery we make makes me revere The Lord all the more and and it reinforces how precious life and knowledge is.
The late Doctor Tom VanFlandern added a few problems to your list in a page at his site: http://metaresearch.org/cosmology/top10BBproblems.asp
99 cents at Amzon, if you have a Kindle (reader).