Basically what I understand is they are saying "Hey, we're observing things that don't make sense to the big bang theory, so maybe there were multiple big bangs and then maybe if there were multiple big bangs there could be an infinite amount of them.. and what we are observing is the previous big bang's light. So we jumbled a bunch of numbers showing this is possible."
But the paper fails to deal with the fact that, yes, if there were multiple big bangs, then maybe the "big" bang isn't really the significant big event everybody has it thought out to be -- there wasn't just one event that created everything. Although it sounds great. So they are just making excuses to keep the big bang theory alive and should instead just say 'we don't know what created the universe' and abandon the 'big bang' theory all together. There own paper disproves the entire big bang theory.
Their paper doesn't "disprove the entire big bang theory."
It does find some problems with the prevailing inflationary model (in which a short period of rapid inflation follows the big bang). Their model gives another way to solve the problems that the inflationary model solved. Other models might also work. And so science proceeds...
I guess I should had made it more clear in my post. Let me try again; if the current theory is stated as such "there once was nothing, and then there was one big bang that created everything in the universe and this was absolutely a single event", and then in the paper they conclude, "oh, wait, there were multiple events", then by extension the theory that everything was a single event -- called the big bang theory -- is no longer a true. No single event, no big bang theory. But no, they decided to interpret the data to fit around the conclusion of the big bang by using fancy names. You can't call something a 'single event' and have it both a 'single event' and 'multiple event' at the same time. It either was a single event or it wasn't! I'm not sure if I could be more clearer. Where is it in my logic can you show me that I am wrong?
Maybe they weren't talking about multiple simultaneous events (although the concept of time doesn't really apply anyway) but more about prior (in the sense of one having an influence on the other) events that had impact on the initial conditions for our current universe's big bang.