Shyan, this may seem a bit odd but what these people are typically talking about is not a "Big Bounce Theory" but rather the standard "Big Bang Theory" (as reporters/popularizers call it) with a slight change in the first fraction of a second---replacing the singularity with a bounce---at the very start of expansion.
Ordinary Friedmann model cosmology is recovered after an extremely brief interval of time, like e.g. 100 Planck time units.
This is explicit in the December paper by Cai & Wilson-Ewing, for example. Coming into the bounce they have a phase which is dominated by matter (for simplicity they include Dark Matter and the usual small positive Λ, it is a standard Friedmann ΛCDM contraction). Then radiation energy becomes dominant (with the shortening of wavelengths).
Then at extremely high energy density,
quantum effects become dominant and the actual rebound occurs.
And then they continue their analysis through the same 3 stages, into the expanding phase: quantum domination, radiation-dominant, matter dominant. And they are back on the familiar ΛCDM standard cosmic model track.
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http://arxiv.org/abs/1412.2914
A ΛCDM bounce scenario
Yi-Fu Cai,
Edward Wilson-Ewing
(Submitted on 9 Dec 2014)
We study a contracting universe composed of cold dark matter and radiation, and with a positive cosmological constant. As is well known from standard cosmological perturbation theory, under the assumption of initial quantum vacuum fluctuations the Fourier modes of the comoving curvature perturbation that exit the (sound) Hubble radius in such a contracting universe at a time of matter-domination will be nearly scale-invariant...
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14 pages, 8 figures
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I don't like calling the standard LCDM cosmic model by the name "big bang theory" and it is not called that in the professional literature. But IF YOU LIKE TO CALL IT THAT then what Cai&Wilson are analyzing here is:
"big bang theory with a bounce"
or "non-singular big bang theory"
It is just familiar old big bang Friedmann equation but with the singularity fixed---with a bounce replacing the failure point of the classical version. Does that make sense? I hope so. Let me know if you have problems with that viewpoint, or would prefer a different terminology.
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