Fun! FWIW, I agree on the database, but no such will be complete/completely satisfying for every user, nor will a vocabulary be rigid and consistent since both language and science evolve. At the same time we are discussing some recent results that has barely settled. I am sure there are popular science resources that are easier to digest, but - with the caveats that peeer review is fallible and scholars can have narrow interests - Scholarpedia comes to mind [
http://www.scholarpedia.org/article/Main_Page ]. If you haven't heard of it, maybe that is a tip. I haven't had time to peruse it much, just when something fits. It has a very nice article on the long term stability of the solar system, by the way.
"quantum cosmology", "QFT, inflatons, inflaton field, magnetic monopole".
Speaking of Scholarpedia, if you want a complete quantum cosmology you may want to look at how linearized gravity can be quantized [
http://www.scholarpedia.org/article/Quantum_gravity_as_a_low_energy_effective_field_theory ]. It may or may not break down in nature - the whole idea of "effective" quantum field theory is that it will under some conditions - but as I just said in another comment: An infinitely large turtle is in principle infinitely much likelier than an infinite series of turtles all the way down* (or up, in energy scale). Else people tend to think of either semiclassical cosmology - keeping general relativity classical - or something like string theory.
Not being a theoretical physicist it is hard to filter out the stuff one shouldn't worry about. My filter need not apply to you, but in case you wonder how I look at it:
- Magnetic monopoles have never been observed, and they arise in theories that are arguable less likely today. "Modern interest in the concept stems from particle theories, notably the grand unified and superstring theories, which predict their existence.[3][4]" [
https://en.wikipedia.org/wiki/Magnetic_monopole ] GUT implies in general that protons decays, but we do not see that. And string/superstring theory imply natural WIMPs that LHC and ACME did not see.
- Quantum field theory, obviously as it is "simply" the relativistic version of quantum mechanics, and the inflation field has both been observed on the other hand. For example. Planck especially sees inflation and the imprint of the field fluctuations that eventually resulted in cosmic background areal spots, spot orientation polarization and cosmic filaments. (The latter which other sky surveys also see.)
- The inflatons were diluted during inflation, and would have decayed right after the field did anyway, and I don't think we can reach those energies in accelerators in near term (or ever). If inflation is eternal, the inflationary field was effectively emptied out of inflatons - its temperature was effectively cooled to 0 K. (Which will take infinite dilution/adiabatic cooling time, but here we may have infinities and eat them too.) And since we don't see inflatons in any case I think the original idea became that these particles were unstable and decayed. The field potential Planck sees looks Higgs like, so presumably any particles during inflation would not have their vacuum state mass like Higgs eventually got - which is why any of them would decay, AFAIU, precisely compliant with the original idea. Maybe it isn't important, there are lots of field excitations that physicists likes to kick around (say, "virtual particles" that have imaginary mass if you treat them like particles and try to derive mass - they are non-resonant excitations, not resonant excitations like bona fide particles).
"Quantum incompleteness of inflation".
Turok is the last author, so his interest would be to do away with inflation so he can make his bouncing universes more appetizing. This is not my specialty, but from the abstract I would deem that they approximate a flat, inflating patch as a de Sitter spacetime and then say something about de Sitter spacetime. Not really convincing.
Here is the fun in this (but maybe it is me just being sophistic): The topology of a de Sitter space time has a bottleneck as in a conic section if you glue two copies together in the narrow end at the Planck scale, to get a smooth topology to study. So of course you run into problems if you go to such scale sizes in a universe that started out that way (at the bottleneck). But we know that the topology of spacetime can be flat if we want to consider a non-bouncing universe. So we can approximate Turok's de Sitter universe with a flat space and that leads to a breakdown of bouncing universe physics in as much as it relies on de Sitter space and that bottleneck and its problems. In such a case, to quote the paper, "new physics is required", preferably something that works in flat space. LCDM cosmology comes to mind.
That said, it is nice to discuss new stuff. But since I did not read Turok et al I was a bit lazy on my part. I hope you have non-lazy fun in your further digging!
* If you take the analogy to biology, it breaks. It works out as equally easy on cell level, exponential growth of population is exponential growth in mass, so it doesn't matter if you build a single turtle or a chain of equal massed ones. Analogies are still analogies, I guess.