Question regarding the validity of the big bounce I have several questions regarding the "big bounce" theory. It appears to be popular among LQG researchers. My questions are as as follows.
1) How one reconciles it with the fact that it is now experimentally established that the universe is expanding in an accelerating manner?
2) The entropy of the universe should have been very very low (maybe zero) at the time of the big bang/ big bounce. What was the entropy "before" that event? Was it even lower? If it was lower then doesn't that mean entropy decreases indefinitely? On the other hand if we accept the entropy was higher then doesn't that violate the second law of thermodynamics?
3) What observational evidence can confirm pre-bounce physics? According to GR there are some points near the bang/bounce where one simply can't easily define time in a meaningful way. Even for a quantum gravity theory, is it possible for any theory to extrapolate itself "before" the "bounce"? If there are no observational consequences after the bounce shouldn't one apply Occam's razor?

 A: 1) Isn't really a problem--aside from inflation, you'd expect matter to be dominating the cosmological constant in the very early universe--we have only recently entered the era where the CC dominates matter.
2) is an open research question right now--no one really knows the answer to this.  I guess the hope would be that the bounce event somehow sorts out microstates or something.  But, to my knowledge, no one, in any field, has really satisfactorily solved the entropy problem in cosmology.  
3) people have talked about there maybe being some sort of fingerprint on the CMB coming from a bounce--I heard talk that there would be rings in the CMB from pressure waves generated by the bounce.  There was a small amount of hubhub when people supposedly saw these rings, which were later dismissed as a confirmation bias problem.  That said, I don't think the phenomenology of this has been taken too far--there may well be observational fingerprints to this that no one has thought of.  
I think you take the claims of people waiting a big bounce too seriously--saying that a model predicts that this can happen is not the same thing as saying that this definitely did happen, and that the model is correct.  And it's not uncommon to have a big picture prediction to precede observational evidence for that big picture prediction.  Even if it turned out that the big bounce was unobservable, this model might still tell you something about the behaviour of plasma heated to Planck temperatures, or something.
A: On the entropic behavior (issue 2): the entropy would behave pretty much as in a big bang scenario at both sides of the bounce. There is no issue with the 2nd law of thermodynamics. The entropy would be minimum at the bounce itself, and conscious beings at either side of the bounce would experience time to increase in the direction the entropy increases (away from the bounce).
A: This connects in some ways to what I wrote in:
Did spacetime start with the Big bang?
The other side of the de Sitter “throat” is a cosmology which implodes.  Now it is important that everyone not take the solutions to Einstein’s field equations literally.  Johannes is right in fact, the entropy increases from the minimal region in the throat with a time arrow heading in opposite directions.  Then according to our time arrow entropy decreases on the “other side.”  This is not different from the white hole part of the Schwarzschild solution.  The white hole horizon rapidly decreases and the entropy declines as well.  However, we do not have white holes in the current state of the universe, so they are not taken as physically the same as a black hole.  They may have existed in the inflationary universe, where the rewind of anisotropy in the reverse time direction might lead to black holes --- or white holes in the forwards time direction.
The other side may correspond to some quantum “anti-universe.”  An electron may be thought to tunnel through a potential barrier by being annihilated by a positron, which in turn is in a pair $e,~e^+$ and the electron on the other side of the barrier escapes free.  This other half of the universe, or “biverse” might be compared to such tunneling.  So this other universe should not be taken in some concrete sense, but more as a QFT or mathematical gadget.
The data does suggest our universe will expand endlessly and will no recollapse.  So the cyclic model appears to be ruled out.  Our observable universe is not likely to recollapse unless there is some unexpected potential function in the mini-superspace which reverses the current accelerated expansion.
A: This question can be related to the linked question as remarked by Lawrence. In that question I mentioned the Penrose CCC theory and it has to deal with exactly the issues in this question. In short the answers are:
1) The Penrose CCC mathematics is independent of the overall K curvature, but it is generally working to the current evidence that the Universe is expanding. Not only that, but surprisingly, the previous universe (aeon) was expanding too! How this can be fitted together is contained in the details of the CCC idea, but a core part is the use of Conformal transformations. Note that the previous aeon lasted for infinite local time (useful in the next point).
2) Penrose has suggested that the information loss connected with Black Holes is responsible for reducing Entropy again. Basically the loss of this matter (in the previous aeon's black holes) reduced the number of degrees of freedom available. So he is postulating that Entropy will balance out come the next Bang. Of course something has to give, and Penrose is comfortable with one consequence that Quantum Unitary does not hold in this Black Hole context.
3) As mentioned in the linked Answer, there is a recent Arxiv paper on analysis of circles in WMAP data, which Penrose claims provides evidence of gravitational radiation from huge black hole collisions in the earlier aeon.
