The Big Bang theory did not allow much room for optimism concerning our future. However, 15 years ago, physicists realized that the theory should be modified because it was plagued by many complicated problems related not only to our future, but to our past and present as well. For example, the standard Big Bang theory combined with the modem theory of elementary particles predicts the existence of many superheavy stable particles carrying magnetic charge: magnetic monopoles. These objects have a typical mass times that of the proton. According to the standard Big Bang theory, monopoles should appear at the very early stages of the evolution of the Universe, and they should now be as abundant as protons. In that case, the mean density of matter in the Universe would be about 15 orders of magnitude higher than its present value of about 10-29 g/cm3
Originally, we hoped that this problem would disappear when more complicated theories of elementary particles were considered. Unfortunately, despite the rapid development of elementary particle physics, the monopole problem remained unsolved, and many new ones have been added: the gravitino problem, Polonyi field problem, domain wall problem, axion window problem, and so on. Physicists were forced to look more attentively at the basic assumptions of the standard cosmological theory. We have found that many of the assumptions are very suspicious.
The main problem of the Big Bang cosmology is the very existence of the Big Bang. What was before the Big Bang? Where did the Universe come from? If space-time did not exist for times less than 0, how could everything appear from nothing? What appeared first: the Universe or the laws determining its evolution? When we were born, the laws determining our development were written in the genetic code of our parents. But where were the laws of physics written when there was no Universe?
The problem of cosmological singularity still remains the most difficult problem of modem cosmology. However, we can now look at it from a totally different point of view. At school we are taught that two parallel lines never cross. However, general relativity tells us that our Universe is curved. The Universe may be open, in which case parallel lines diverge from one another, or it may be closed, and parallel lines cross each other like meridian lines on a globe. The only natural length parameter in general relativity is the Planck length lp approximately 10-33 cm. At smaller distances, the standard concept of space becomes inapplicable because of large quantum fluctuations. Therefore, we would expect our space to be very curved, with a typical radius of curvature about 10-33 cm. We see, however, that our Universe is just about flat on a scale of 1028 cm, the radius of the observable part of the Universe. The results of our observations differ from our theoretical expectations by more than 60 orders of magnitude!
Why are there so many different people on Earth? Well, Earth is large, so it can accommodate a lot of people. But why is Earth so large? (In fact, it is extremely small compared with the whole Universe.) Why is the Universe so large? A typical answer is that the Universe is large because it is a Universe, so it should be large, should it not? However, let us consider the Universe of a typical size lp just emerging from the Big Bang. Let us assume that this Universe had the greatest possible density at which we can still describe it in terms of usual space and time. This is the so-called Planck density, 1094 g/cm3, which corresponds to matter consisting of particles displaced at the Planck distance lp from each other. We do not know how to describe matter with a greater density. But if we take the Planck size universe with the Planck density, we can easily understand, by definition of the Planck density, that such a universe can contain only a few particles. The standard assumption of the Big Bang cosmology is that the total number of elementary particles in the Universe almost does not change during the expansion of the Universe. Thus, a typical universe should contain one particle, maybe ten particles, but not 1088 particles, which is the number contained in the part of the Universe we see now. This is a contradiction by 88 orders of magnitude.
The standard assumption of the Big Bang theory is that all parts of the Universe began their expansion simultaneously, at the moment t = 0. But how could different parts of the Universe synchronize the beginning of their expansion if they did not have any time for it? Who gave the command?
Our Universe, on a very large scale, is extremely homogeneous. On a scale of 1010 light years, the distribution of matter departs from perfect homogeneity by less than 1 part in 100,000. For a long time nobody had any idea why the Universe was so homogeneous. But those who do not have good ideas sometimes have good principles. One of the cornerstones of the standard cosmology was the cosmological principle, which asserts that the Universe must be homogeneous. However, the Universe contains stars, galaxies, and other important deviations from homogeneity. We have two opposite problems to solve. First, we must explain why our Universe is so homogeneous, and then we should suggest some mechanism that produced galaxies.
All these problems (and others) are extremely difficult. That is why it is very encouraging that most of these problems can be resolved in the context of one simple theory of the evolution of the Universe — the inflationary scenario. Meanwhile, some of its consequences are even more surprising. Instead of the Universe looking like a single expanding ball created in the Big Bang, we envisage it now as a huge, growing fractal consisting of many inflating balls that are producing new balls that are producing new balls, ad infinitum.
--The Origin and Evolution of the Universe, Ben Zuckerman, Matthew Arnold Malkan, Chapter 7: Future of the Universe