A singularity I think is in principle infinitesimal and infinitely dense, but in practice that may not be accepted. I think you raise a good question but I don't know what the criteria (if any) for big bangs are supposed to be.
There's been an idea of naked singularities dying and consuming space time around it at the speed of light, one that Hawking and Stewart 1992 got from running their model through a computer. They themselves and most apparently don't seem to believe in this result. One who does
http://arxiv.org/abs/gr-qc/9312009v1 puts it as a local micro catastrophe, but apparently physicist Poisson accepts it in
http://www.skyatnightmagazine.com/viewIssue.asp?id=1096 as a sort of danger in the universe in general. Perhaps how much of the effect depends on the singularity mass.
Such
unstable naked singularities were thought quite plausible to emerge from LHC in
http://arxiv.org/abs/hep-th/0110255 and
Quote:
We should however add that the present literature does
not reliably cover the case of such tiny naked singularities and their actual phenomenology is an open question
Anyway I can hear CERN say that cosmic rays strike us all the time not that they ever even considered this (they avoid this last paper - that includes 30 yr black hole lifetime - like the plague). In the cosmic ray case the collapsing naked singularity travels at virtually the speed of light, which isn't quite the same thing. Plaga agrees with me that questions remain about the safety of such a prospect. You'd have thought that such an expert on cosmic rays would have/ or would be listened to by CERN.
The trouble is, authors like CERN and that of the last paper I gave, seem to regard LHC research as necessary science, so they narrow or exclude their considerations for risk as a result.