"Big-bang" versus "Big bang"
I spend a good bit of time thinking about what happened in the period of time between the Big-Bang and the Big-Bang. No, I'm not crazy (or at least not with respect to this issue). Rather, the problem is that the term "Big-bang" is often used -- both by professionals in the field and in the popular press -- to discuss two quite different things.
One thing is the "big bang theory" or "big-bang model" in which the observable universe expanded and cooled from a nearly uniform, ultra-hot and ultra-dense bath of radiation and a smattering of particles. This theory is very well-confirmed observationally, back to temperatures of billions of degrees (at which times the model can be probed via nucleosynthesis).
The second thing is the "big-bang singularity" by which is generally meant an early-time edge of the spacetime region that can be treated using the reasonably well-understood physics of classical general relativity and quantum field theory.
These two different ideas are conflated because in the original formulations of "big-bang cosmology" these notions went hand-in-hand: extrapolating the big-bang theory back in time led inexorably to the big-bang singularity. And singularity theorems proven by Hawking, Penrose and others made this connection quite tight by showing that under what seemed like rather general conditions, the initial singularity is unavoidable.
However, in the modern cosmological theories developed over the past 20 years (inflation, and also many of its rivals), this connection does not exist. In particular, in inflation the creation of a hot, homogeneous region occurs through 'reheating' at the end of inflation, but may happen an indefinite time after an initial cosmological singularity -- if there even was one! Moreover, nearly all of the classic singularity theorems fail to apply to inflation because they assume properties of matter (essentially that it is gravitationally attractive) that inflation violates.
Thus when discussing inflation -- or the cyclic model, etc. -- it is crucial to distinguish between these meanings. Otherwise you get a lot of rather frustrating debate (see this for a current example) about whether we can gain evidence of what happened "before the big bang". If this means "before a hot, homogeneous radiation-dominated phase", then the answer is clearly yes: the current CMB tests of inflation are doing exactly that. If "before the big-bang" means before some cosmological singularity, this is a very different proposition, and the answer may or may not be yes, and depends a lot on what sort of singularity you are talking about.
Some of the most interesting cases lie in between. For example, believers in the string theory landscape (among others) believe in a picture in which inflation occurs eternally, and creates infinitely many "bubble universes", each of which is spatially infinite inside. The genesis of one of these bubbles is not quite a big-bang in either of the above senses, and yet entails the "creation of a universe", and there are fascinating questions about whether other bubbles would have any observable in ours (I think perhaps they might)
So I'd like to make two pleas. First, let's all try to make this distinction clear both within the scientific community and in communications with the general public. We don't do ourselves any favors by having newscasts etc. discussing how cosmologists are debating "whether there was a big-bang" when they all agree on the basic cosmological model and are debating, say, the cyclic versus inflationary cosmology. (Imagine biologists debating lateral transfer of DNA and calling it a debate about whether evolution happened...not wise.)
Second, to make this easier, we could use a new name for a huge, hot, homogeneous, region that could in principle evolve into our universe, however it was created. I've recently used the term 'hotzone'. 'Hotpocket' might be better but runs into trademark issues and does not accord the creation of the universe the respect it deserves (with all due respect to the folks at Nestle foods). But I there have got to be better ideas out there. Any proposals?