There are several serious fundamental flaws fully acknowledged by everyone in the field with even the basic Big Bang theory. It’s why inflation theory was invented —to explain away the flaws. However, inflation theory is even more controversial. Many prominent people in the field of cosmology don’t like the theory. They say it’s too contrived and easy to manipulate the numbers.
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
The Inflationary Universe
The preceding problems with the big bang can be alleviated all at once (at least in principle), by a new kind of cosmology called the inflationary universe.
http://www.freerepublic.com/focus/f-news/3108562/posts?page=17#17
"Afterward, of course, when people found out how to take into account correctly the spin of the electron, the discrepancy between the results of applying Schrodinger’s relativistic equation and the experiments was completely cleared up.
"I think there is a moral to this story, namely that it is more important to have beauty in one’s equations than to have them fit experiment. If Schrodinger had been more confident of his work, he could have published it some months earlier, and he could have published a more accurate equation. That equation is now known as the Klein-Gordon equation, although it was really discovered by Schrodinger, and in fact was discovered by Schrodinger before he discovered his nonrelativistic treatment of the hydrogen atom. It seems that if one is working from the point of view of getting beauty in one’s equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one’s work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further developments of the theory." --Paul Dirac
And how can one have beauty without God in one's life? It seems a non-sequiter.
I believe God derived the function we discovered as mathematics. If He hadn't, these sentences could never have been read here as there'd be no one to read them anyway.