In this book, Sean Carroll aims to connect the most mundane phenomena from the everyday life such as the scrambling of eggs to the most speculative concepts in cosmology such as bubble universes where time runs backwards. Of course, science has shown that no such relationship exists - even though it may be attractive for some really ambitious armchair physicists - so Carroll fails. But it may be interesting to look at this failure in some detail.
To make the book "cooler", Carroll has used various random characters such as Miss Kitty, a cat who hides under its sofa, and Brad Pitt who grows younger with time (as F. Scott Fitzgerald told him to do in "The Curious Case of Benjamin Button"). The storylines were largely absent and they didn't help to shed light on the highly controversial scientific points, either. The same seems to be true for several quotes - such as those from St. Augustine. I suspect that the author only wanted to superficially "connect" with the lay readers and broader audiences. After all, the same thing can be said about the title which is a mutation of the title of a famous novel by James Jones.
Carroll occasionally writes some things about physics of time that are correct. At any rate, the main scientific goal of the book is to argue that the irreversibility of the phenomena around us (e.g. that we get older and never younger) is a consequence of some details in the history of our Universe. We must live in a bubble Universe surrounded by other bubbles where time runs backwards and where many other logically inconsistent phenomena take place.
Carroll never shows why he thinks that the asymmetric scrambling of an egg is linked to any of those crazy speculations about our cosmic pedigree. In fact, we can't blame him for his failure. Nothing like that can be explained because no relation of this sort exists. Even for a good writer, it would be hard to demonstrate something that is so fundamentally untrue.
The irreversibility of time is related to the so-called second law of thermodynamics - to the increasing amount of disorder of any isolated physical object (increasing entropy). And this law can be proven and has been proven more than 100 years ago. The entropy of objects is related to the statistical properties of a large number of atoms (inside the same egg - the rest of the Universe and its history is irrelevant, because of the "locality" of the laws of Nature). Undergraduate students have been correctly learning that thermodynamics (gross observations about the heat, temperature, and irreversibility) may be derived from statistical physics (mathematics applied to many atoms) for a century. Unfortunately, Sean Carroll didn't listen to his teachers because he apparently thinks that thermodynamics is a consequence of some details in cosmology. He has missed the main point of statistical physics.
There is nothing unnatural (or even paradoxical) about the low value of entropy in the past. Quite on the contrary, it is a consequence of the second law that guarantees that the entropy increases. We know that the entropy used to be lower and we know that it agrees with all other laws of physics that have been empirically validated.
The proof of the increasing entropy due to Ludwig Boltzmann (who later committed suicide, being surrounded by people not unsimilar to Carroll himself who were unable to appreciate the depth and validity of his key insights into thermodynamics) also uses a pre-existing logical arrow of time but there is nothing wrong about it. The logical arrow of time - saying that we may remember the past and not the future - belongs to the logic of any conceivable world with "time" that qualitatively resembles ours. No world with "observers" can exist without it.
While the microscopic, exact laws of physics may be time-reversal symmetric (they don't distinguish the past and the future) or at least CPT-symmetric (ignore the acronym if you don't know what it means), the logic how we apply them in the presence of unknown data always "discriminates" the past from the future. For example, if you calculate the probability that a particle decays into a pair of particles and you don't specify the spins, you must sum the probability over the final spins (because you don't "care" about them) but you must average over the initial spins (because you don't "know" them).
Summing is something different than averaging - and the past therefore differs from the future. And this asymmetry - an extra denominator preferring a larger number of states in the future than in the past - automatically implies that the entropy increases. The role of "assumptions" and their "consequences" in logic is asymmetric. And in the same way, whenever there is any incomplete information, the past and the future play an asymmetric role, too - because by the very definition of the words, the past is described by the "assumptions" and the future is about their "consequences". Because there's no symmetry between the assumptions and their consequences, it's also impossible to mix the two arrows of time inside a bigger multiverse.
Also, in a striking contrast with Carroll's text, the methods to retrodict the past are completely different than the methods to predict the future. To predict the future is "straightforward" - quantum mechanics tells us the probabilities. However, to reconstruct the past, we must choose competing hypotheses, assign them with (somewhat arbitrary) priors, and do the logical inference. The answer - our retrodiction - is not unique. But when we do it correctly, we may see that the entropy in the past was lower than today.
Most of the mysterious properties of the bubble Universes discussed by Carroll are even more impossible than the ordinary "time machines" and "wormholes" from some conventional popular books. If there exists a contest looking for a professional physicist who prints and sells a book promoting the most scientifically nonsensical phenomena and relationships between them, Carroll is a new hot candidate.
The science in the book makes no sense and the purpose of the book is for the author to show how he can make science popular. Except that it isn't science and I guess that it won't get too popular, either, because the references to the popular culture are excessively cheap, chaotic, and out-of-touch even for highly undemanding readers. Finally, let me say that you should largely ignore the unhelpful votes under the unfavorable reviews because the author uses his blog to distort the public perception of this very strange book.