Newton's third law is probably the single most misunderstood concept in all of Physics - I have seen more than a couple of Physics undergrads conceptually misunderstand it. The problem, I suspect, is rooted in the way the idea is commonly framed in language: the concept of "action", and especially "reaction".
The trouble is that most people relate these words to their everyday use, where it is used in the sense that an event, an "action", triggers another event, the "reaction", i.e. causality between the events is implied. So a lot of people seem to understand the law in this abstract sense: if A exerts a force on B, B "reacts" with an equal but opposite force on A. If I push the wall, the wall "pushes" back on me, equally. We produce a force A, which causes an equal and opposite force B.
But that statement is actually complete nonsense. Well not quite. Unfortunately, that conceptually wrong understanding of the law is mathematically equivalent to the correct one anyway and this is likely why the misunderstanding is so common: you can get away in your Physics classes with a misunderstanding of the law.
Here is a much better way, in my opinion, of framing Newton's third law: a force is a mutual interaction. Another way to put it would be: forces only exist in mutual interaction pairs.
You see, when I push against the wall, my hand and the wall push against each other, and that is the "mutual interaction". The key point I am trying to make here is that the forces A and B are simultaneously caused (caused by the individual doing the pushing) whereas with incorrect understanding A causes B.
If you have what in Physics culture is sometimes called "Physical intuition", this understanding of the third law should be "obvious". Why is why I always tell people that if you don't intuitively understand Newton's third law, you don't understand it at all.
Most people seem to understand the other two laws but Ill tell you guys a secret: Newton's 1st and third laws are actually pretty useless (but hey, we have to teach high-school kids something about Physics after all). The first law is already subsumed by the second law and the third is not "fundamental", i.e. it can actually be derived from another idea. That idea is the conservation of momentum (which is also not fundamental because it can in fact be derived from the idea of translational symmetry in space).
In fact, it also turns out that force is a pretty redundant concept because it is defined as the rate of change of momentum so all we need again is just momentum. This is why when you get to more advanced Physics, i.e. the standard/level of the Lagranian/Hamiltonian formulations of classical mechanics and above, we completely do away with the concept of force and Newton's laws, and only talk about conserved quantities like momentum, energy and angular momentum. Oh and another thing, Newton's first two laws only hold in an "inertial frame of reference" meaning only in a non-accelerating environment (when you're standing on a bus and it speeds up/down or turns, from your point of view, the first two laws are violated) and the third law doesn't hold at all in relativistic mechanics when you bring fields into the picture (but momentum conservation does).
So to answer your question: Newton's laws don't really have anything to do with the BBT. I mean yes, things like momentum and energy and their conservation (which are the real fundamental ideas of Physics) do have a lot to do with the details of the Physics used in the theory and in cosmology in general. But if you really, want to understand the subtle details of cosmology, you have to study general relativity. I would recommend some popular Physics books but the problem is that popular Physics is mostly worse than f-cking useless because most of it ends up actually obscuring the Physics more than anything else (I read a lot of popular Physics as a teen, then went on to study Physics and found that most of what I had learned from popular Physics was garbage), or is about fancy mathematical science fiction like string theory.
If you really want the answers to the "interesting" questions with regard to the BBT (and I suspect "interesting" for most people would be "why" type questions), you need to read or talk to a "philosopher of Physics". And once you do, even if understand all the Math and Physics as well, you'll find that what they tell you is just verbiage and more questions.
