Is the "Radiation Paradox" a problem for a Cyclic Universe? 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??
 A: 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".
A: 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.
A: 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.
A: 
If the collapse ends in a bounce, the cosmic radiation is still there

No.
If we look at universe chronology we will see that Lepton epoch has lasted between [1..10] seconds interval after BigBang. Then most leptons and anti-leptons has anihilated, producing bunch of photons, so this has started a Photon epoch where photons mostly dominated universe mass-energy in time period [10 seconds ... 370,000 years] after BigBang. 
Now if we will respect time-symmetry principle in Physics, which we should I think, then constantly collapsing universe will raise average temperature of universe until there will be left about 10 seconds to full compression up to singularity. From this point temperature  of energy soup will be so high, that according to Einstein $E=mc^2$ principle energy (photons) will start to convert back into matter, namely - there will be going a pair-production process $\to$ electron-positron generation from photon :
$$ \gamma \to e^- + e^+ $$
Or if you want a Feynman diagram of this process, it will look like :

(a) is plain electron-positron pair production from photon and (b) is very similar process, just additionally yet another photon is generated too (but this resulting photon $\gamma^{\prime}$ energy will be lower than incoming photon energy for respecting energy conservation law). When universe collapses further probability of (b) should decrease, because due to high temperature resulting photon will gain additional energy, thus further collapsing into electron-positron.
So in the end - universe will be mostly dominated with leptons and anti-leptons back again. Up to this point, photons will be left just as a smell from a tasty dish. And almost all cosmic radiation will be gone, so any information which was encoded into CMB will be lost and not transferred into next BigBang. Next BigBang will start completely as a new event and will not carry any information from previous universe phases. In addition to that, there is some risk/probability that next BigBang will not look like current one and maybe Physics laws will be a bit different than currently are now. Nobody knows for sure.
EDIT
Actually even now some research suggests that laws of Physics are not isotropic in a universe. Scientists have aggregated data from a very distant objects (a quasar 13 billion light years away) and detected that there is a tiny variations in the fine structure constant along some axis in a universe. So universe may be some kind of dipole - has North and South poles along which electromagnetic force strength (law) varies, but it  does not in perpendicular direction. If it's true, being sure by 100% about any particular collapse/explosion scenario would be more unfair. What a mess !
A: 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..."

