Is the "Radiation Paradox" a problem for a Cyclic Universe?

The explanation does not make sense because a cyclic universe would be completely opaque at the time of the big bounce. It says nothing about the hypothesis that the universe could be cyclic.

In the period close to the bounce, light will be blue shifted by a very large shift $z$. It will freely participate in matter-antimatter creation and the singularity will create and identical initial condition for each cycle in the model.

The same applies to arguments concerning increasing entropy. The second law of thermodynamics applies to isolated systems within the universe. It cannot be applied to the universe as a whole. Entropy is closely related to energy, which is the time component of a vector. Vectors only have local definition in general relativity, there is no way to sum and find the "energy of the universe" or the "entropy of the universe".

In my view the main logical fault is assuming that we'd be able to count the number of cycles elapsed so far, or that a certain number of cycles ought to have been completed by now.

A cyclic theory necessarily implies that there are processes which reverse or relieve any accumulated products of past cycles, therefore being able to observe only a small number of past cycles (or not being sure how many cycles had completed, only being sure that the evidence suggests they have been few in number) would be as much evidence for the theory as against it.

A perfectly cyclic process stores no intrinsic record of how many cycles have elapsed, because record-keeping requires a non-cyclic process (or at least it requires the records to be recycled on a much longer cycle than the cycle under observation). If the records were equally cyclic with the cyclic process being measured, then for every swing of the pendulum forward which creates the records, the backswing erases the records and restores the initial conditions of record-keeping.

Generally speaking, what makes a cosmic cycle a cycle is that it destroys all the characteristics of the previous cycle, such as whether energy is in the form of electromagnetic radiation or something else. So the technicalities of the pseudoscience article are naive and false.

But what about the conclusion? Roger Penrose is famous for developing the twistor theory used extensively in studying particle-particle interactions. He has also developed a cosmological theory of what he calls the conformal cyclic universe (A layman's introduction is provided as his book, Cycles of Time). He tentatively predicted that certain aspects of the previous cycle would in fact show up in the next - not in their original form but as circular distribution patterns of matter and/or energy in the sky. He and colleagues looked for such telltale rings but found none.

Although the preliminary search was negative, this does not disprove the whole conformal cyclic theory. It remains an open possibility that the Universe might be cyclic and, further, that something identifiable could leak through from the previous cycle. However the idea that this something will survive multiple cycles, so that we could count them like tree rings, has no foundation whatsoever. So the pseudoscientist's conclusion is also unsound.

Recently I found out that someone had already responded to this silly paradox. Quentin Smith wrote the following:

"One model that [was not mentioned] is A. D. Linde's oscillating model. He developed a new oscillating model, not the old one that was developed in the early 1960s... Linde came up with a new theory of this, for which there's no good counter–argument. I'll wax technical for a couple of sentences and give you a rough idea of what I mean. There are four forces in nature—the strong force, weak force, electro–magnetic force—and there are coupling constants for each of those three forces, and we have theories of those, and they're workable. Now A. D. Linde shows that by analogy there should be a coupling constant to the gravitational force, and given that, this will solve all the problems of an oscillating universe that have ever been brought up. For example, one problem is that, if the universe oscillates, if it goes through a Big Crunch and expands again, then all the radiation from a previous cycle will accumulate in the next cycle, and as that one expands it'll get larger still because it will have more radiation from all the energy in its stars, and eventually you'll get to something that's so big it'll expand forever, and then you'll no longer have an infinite number of oscillating universes. But A. D. Linde’s theory shows that all this excess radiation from the cycle that's contracting before it hits the big bounce, when it gets near the so–called Planck era, which is about 10⁻⁴³ seconds, a very short time before it begins to bounce out again, all the entropy, the disorder that's built up in the previous cycle, and all the excess light and radiation that comes from the stars is lost. So in each new cycle we begin anew, the new Big Bang, and so his theory solves all the existent objections against an oscillating universe that's infinitely old..."