Now that the BICEP2 has given us evidence close to the alleged big bang singularity, Matt Strassler and Lubos Motl have reopened the debate about whether there really is a singularity. Those are sensible mainstream views. Others will push back harder, and speculate about before the big bang and into the multiverse.
I have to agree with Strassler that the evidence points to energies high enough that our physical theories break down, so we cannot go further. I also agree with Tegmark that we never observe true singularities in nature. I am a positivist, and I believe in what has been demonstrated. Infinities and singularities are wonderful mathematical tools, but math is not the same as physics.
Depending on how the inflation evidence plays out, I am not sure the big bang has anything to do with general relativity or a spacetime singularity. The physics was not dominated by gravity or the standard model, as we know them. Something mysterious called an inflaton field was releasing huge amounts of energy. I am not even sure about the reports that BICEP2 saw gravity waves. Maybe they saw inflaton waves. Some physicists have said that this proves gravity is quantized. I don't know how they can say that, when no one knows what the inflaton is or how it relates to gravity.
I expect the meaning of BICEP2 to be settled in the next year or so, but unwarranted speculation about time and multiverses to go on for the foreseeable future.
Update: Strassler argues:
Who is still telling the media and the public that the universe really started with a singularity, or that the modern Big Bang Theory says that it does? I’ve never heard an expert physicist say that. And with good reason: when singularities and other infinities have turned up in our equations in the past, those singularities disappeared when our equations, or our understanding of how to use our equations, improved.Lumo responds:
Moreover, there’s a point of logic here. How could we possibly know what happened at the very beginning of the universe? No experiment can yet probe such an early time, and none of the available equations are powerful enough or usable enough to allow us to come to clear and unique conclusions.
But by endorsing the idea that the Big Bang singularity exists, we don't claim that the classical general relativity is exactly accurate and all of its conclusions about quantities' being infinite at the singularity are strictly right. We never mean such things.