RowRow said:
Mostly I would like to know how far has science come to understanding what happened before the big bang...
That's a question about our own past. Like any question about the past it is accessible to scientific investigation using mathematical models. That is how we know the past---we extrapolate back in time using models fitted to presentday observed data. And people are doing that kind of research--building those kinds of models.
Models and computer simulations that go back before the start of expansion, to a prior contraction, have been and are being constructed. It's a growing field of research--a good keyword is "bounce". A growing number of people work on bounce cosmologies, or more generally "non-singular" cosmologies----models which don't have a breakdown point called a singularity but get around that earlier blow-up or failure in various ways.
Nothing definite will be known until some of these new models are
tested.
So far the leading bounce cosmo models simply duplicate the classical predictions, and match the reality which we see.
To be accepted, one or more of the new models must be able to make
better predictions than we can get from the classical 1922 Friedman model cosmology that we are using today. (It is amazing but cosmology still using the ancient Friedman-Lemaître expansion model, which blows up right at the start but otherwise gives very serviceable results.)
So the bounce cosmologists are busy trying to derive prediction about CMB detail which has not yet been seen, and the European Space Agency just sent up a new spacecraft called Planck which has started observing the CMB looking for more detail.
CMB means cosmic microwave background. It is the oldest light, going back to year 380,000 of the expansion.
The way the expansion began is reflected in the map of that CMB light. If bounce or any kind of nonsingular cosmo model can predict new detail in that CMB map, then it will gain credence. Then we will be able to say we know something about the before-bang past.
A new book on pre-Bang by the world experts on this line of research is scheduled to come out late this year or early next. The publisher is Springer, the editor is Rudy Vaas.
In general I would avoid anything that says "Multiverse" in the headline because you asked about our past, not some hypothetical alternate universe
This book has some 20 leading authorities as authors. A few of them are "multiverse" thinkers, but they are not typical or a majority. The book is called
Beyond the Big Bang. I would rather the editor had been more selective and left the multiverse stuff out. I will look at it in the library but probably not buy a copy. Other pre-bang books will be coming out, I feel confident, that will focus more on my particular interests.
If you want to see the most highly cited technical research on pre-bang here is a list of post-2006 papers ranked by number of citations.
The top 20 are almost all bounce-type. This is not to read, just to give a firsthand glimpse of current research.
http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+DK+QUANTUM+COSMOLOGY+AND+DATE+%3E+2006&FORMAT=www&SEQUENCE=citecount%28d%29