I found a criticism of the cyclic universe theory in a pseudoscientific book. The author called the problem "Radiation Paradox." This is a quote from the book:
There are two kinds of light (i.e., electromagnetic radiation) in the universe right now: (a) the famous Cosmic Background Radiation (CBR) left over from the big bang (and discovered by Penzias and Wilson), which has a rather featureless spectrum called a “blackbody spectrum,” and (b) light from various other sources, primarily stars, which has a very complicated spectrum. Right now, in our universe, about 99 percent of the light is in the cosmic radiation and 1 percent is in starlight. In every cycle of the universe, during the expansion phase, stars are formed and emit light. If the universe then enters a collapsing phase, this starlight gets scattered, reabsorbed by matter, and re-emitted many times. This basically homogenizes it into a blackbody spectrum, and it gets folded into the cosmic radiation. If the collapse ends in a bounce, the cosmic radiation is still there and is released in the big bang of the next cycle, whereupon it becomes the cosmic radiation of the next cycle. So, in each cycle the cosmic radiation includes all the starlight emitted in all previous cycles, whereas in each cycle the only starlight present is that produced by stars during that cycle.
Therefore, if there have been, say, a thousand cycles before now, there should be at least a thousand times more light in cosmic radiation than in starlight. If there have been a million cycles, there should be at least a million times more light in the cosmic radiation than in starlight. As we have seen, however, observations show that in fact there is only about a hundred times as much light in the cosmic radiation as in starlight. So there cannot have been many more than a hundred cycles in the past, which implies that the universe has not been cycling forever, and that (in the bouncing universe scenario) the universe must have had a beginning.
Does this make sense to you? Do you think this proves the cyclic universe cannot be correct??