atyy said:
He is going to describe how the effect of the existence of the universe before the big bang would have consequences that remain observable to this day - and which would distinguish such a theory from our current best.
Predictions! Really?
Well in terms of the amount of research being done and the citations to it,
objective criteria in other words, I guess you could say that the LQC that Bojowald is talking about IS our
current best theory of how our expanding universe got started.
At least if by "current" you mean "since 2005" or so.
Folks have been working on the LQC bounce picture since 2001. It does appear able to make predictions about what we can observe in the present (e.g. with the Planck spacecraft ) which would distinguish it from our current NEXT best.

Or next next best, or in any case from various alternatives, if the alternatives made any predictions.
The alternatives are things like Linde's eternal inflation, Steinhardt's brane clash, Hawking's ideas of the 1980s, Veneziano stringy "pre-big-bang" scenario of the 1990s. The alternatives to LQC either are not currently being much worked on, or are rather nebulous and don't make much in the way of prediction.
To recall what Bojowald says about it, I'll put the two snippets of translation together as they appear in the introduction.
==quote introduction==
...Above all, what we've seen in the last few years has been numerous significant indications of its characteristics which can actually be analyzed. The situation, as so often happens in research, is like the beginning stages of solving a jig-saw puzzle---in which one might perhaps guess the final picture, but nevertheless could still be on the wrong track.
Our current picture indicates what a completion of the physical theory can accomplish: It allows us to see what could have happened during and even before the Big Bang. We obtain insight into our universe's earliest prehistory and for the first time are able to analyze how it actually arose.
This book will describe not only of the most recent theoretical results but also the observations in space planned for the near future---and it will show how radically they could change our picture of the world. In the case of loop quantum gravity, one of the current approaches combining General Relativity with Quantum Theory, assumptions allow for a nonsingular description of the Big Bang. In this framework, the universe existed before the Big Bang, and one can roughly estimate how its characteristics then may have differed from those at present.
Through its influence on subsequent phases of cosmic expansion, as detected by sensitive instruments, one can probe the prehistory of the universe.
==endquote==
Here's the spires search for "quantum cosmology" papers since 2005:
http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=dk+quantum+cosmology+and+date%3E2005&FORMAT=WWW&SEQUENCE=citecount%28d%29
If you look at the top 50 or 75 papers they are almost all LQC. There are a couple by Hawking and Hartle that made it into the top 75 (they are numbers 57 and 60). Very few Steinhardt ("ekpyrotic" or "cyclic" brane clash) papers.
You may want to expand the search and see what is going on in more detail.
I think objectively what we have here is arguably "current best". I'll post the German original in case anyone wants to check the translation against it.
marcus said:
==quote from original German edition of Before the Big Bang==
...Was wir aber vor allem in den letzten Jahren gesehen haben, sind zahlreiche vielversprechende Indizien für ihre Eigenschaften, die bereits analysiert werden können. Die Situation, wie so oft in der Forschung, gleicht dem Anfangsstadium eines Puzzle-Spiels, in dem man das endgültige Bild vielleicht teilweise erahnen kann, dennoch aber auch auf einem Irrweg sein könnte. Unser derzeitiges Bild deutet an, was eine Vervollständigung der physikalischen Theorie bewerkstelligen kann: Sie erlaubt uns zu sehen, was während und sogar vor dem Urknall geschehen sein könnte. Wir erhalten Einblick in die früheste Urzeit unseres Universums und können erstmals analysieren, wie es wohl entstand.
In diesem Buch werden sowohl jüngste Resultate der Theorie als auch für die nähere Zukunft geplante Beobachtungen I am Weltraum erläutert, und es wird gezeigt, wie radikal sie unser Weltbild verändern können. Insbesondere mit der Schleifen-Quantengravitation, eine der Varianten, die derzeit für eine Kombination von Allgemeiner Relativitätstheorie und Quantentheorie gehandelt werden, sind Ansätze für eine nichtsinguläre Beschreibung des Urknalls erzielt worden. In diesem Rahmen existierte das Universum schon vor dem Urknall, und es lässt sich grob abschätzen, wie es sich damals in seinen Eigenschaften von den jetzigen unterschieden haben könnte. Durch den Einfluss auf spätere Phasen der kosmischen Expansion, die empfindlichen Beobachtungen offenstehen, kann man diese Urgeschichte des Universums untersuchen.
==endquote==