This is some cosmology for laypeople. Specifically, the authors are introducing a new theory of cyclic universes as an alternative to the big bang with inflation model that is currently the received view. They're obviously excited by the research (which they appear to be leading champions of) but also cautious about a theory that so far is observationally indistinguishable from the competition.
It's a fairly easy read, with no mathematics and a fairly slow buildup of jargon. The theory is fascinating too, and I can understand the feeling that it is more elegant than inflation (at least, as they presented it here). It's the idea that the universe is a n-dimensional membrane that is paired with another across a microscopic extra dimension. I've come across this before, as an explanation for dark matter (in this case, the dark matter is in the companion space-time: undetectable by radiation but gravitationally interacting). They focus more on the way that this generates a model for the existence of the cosmic background radiation, expanding space and a variety of that sort of cosmological mystery. Essentially, it comes down to the two membranes crashing into each other periodically, then bouncing back for a trillion years or so before they collide again - which smashes everything into an immensely hot soup of basic particles before cooling down into stars and so forth again.
It's also rare to read popular science that is so cutting edge - normally it is about stuff that is much more settled than this.