Some cosmologists (scientists who study the origin and structure of the universe), particularly those who hold to a naturalistic worldview, don't like the Big Bang because it strongly supports theism. They've thus been casting about for a plausible alternative ever since the Big Bang was first suggested back in the 1920s.
Most, if not all of these alternatives depend somehow on the universe being eternal, that is, infinitely extended in time, but there's a very serious, if not fatal, mathematical problem with theories which posit an infinite temporal extension: Infinities are useful conceptual tools in mathematics but for reasons Physicist Kirk Durston explains, they are difficult to imagine existing in the real world.
Durston writes:
A mathematical infinite past is certainly no problem with mathematical models, but in the real, physical world, it is impossible to “count down” an infinite number of actual years, one at a time, from minus infinity to the present.If we can't start at the present and count backwards to infinity, neither can we start at infinity and count forward to the present. Counting from past infinity to the present is just as impossible as counting from the present to past infinity.
In the real world, an infinite past means that if you were to set this current year as t = 0 and count backward into the past, there would never be an end to your counting, for there is no year in the past that was the “beginning”. No matter how long you counted, you would still have an infinite number of years ahead of you to count and, if you were to look back at the set of years you have already counted, it would always be finite. Always!
Imagine that we have counted from the present back to any arbitrary number of years - a million years, a trillion years - how much further do we have to go to reach the beginning of an infinitely old universe? We still have an infinite number of years to go. So how long would it take to count from the infinite past to a point, say, a million years ago? It would take an infinite number of years! We could never arrive at any finite point in the past if the universe is infinitely old.
As Durston states:
[I]f the past is infinite, actual history would never, ever make any progress at all in getting closer to the present, or any other arbitrary point in time at a finite distance from t=0. There would always be [an infinite number of] years to go.And if there was a beginning it's reasonable to assume that there was a cause of that beginning. Moreover, whatever caused the beginning of the universe, it's reasonable to assume, must have been outside the universe of space, matter and time, i.e. transcendent. It must have been non-spatial, immaterial, and eternal, and, if it's eternal, it's reasonable to assume that it still exists.
Yet here we are. This can only be possible if the past is not actually composed of an infinite number of years. The set of years in the past must necessarily be finite (as opposed to infinite), which means there was a beginning, as science also seems to indicate.
The cause of the universe, it also seems reasonable to assume, must be very powerful and very intelligent to cause such a vast and incredibly fine-tuned and elegantly mathematical universe to come about.
Furthermore, if the cause is intelligent and since it has produced personal beings we can think it reasonable to assume that the cause itself is personal.
No wonder non-theists resist the notion of a finite universe, one that had a beginning and thus a cause. If a finite universe leads to the conclusion that it's reasonable to believe that the universe has a transcendent, immaterial, personal, extremely powerful, extremely intelligent cause then it's hard to see how naturalism, or atheism, is a more reasonable or rational position.
For a fuller explanation of the concept of infinity in the context of the age of the universe see Durston's article. It's not long and it's very helpful.