"All that matter ... in one Big Bang ...," & other cosmological
  singularities
  The first part of this paper contains a brief description of the beginnings
of modern cosmology, which, the author will argue, was most likely born in the
Year 1912. Some of the pieces of evidence presented here have emerged from
recent research in the history of science, and are not usually shared with the
general audiences in popular science books. In special, the issue of the
correct formulation of the original Big Bang concept, according to the precise
words of Fred Hoyle, is discussed. Too often, this point is very deficiently
explained (when not just misleadingly) in most of the available generalist
literature. Other frequent uses of the same words, Big Bang, as to name the
initial singularity of the cosmos, and also whole cosmological models, are then
addressed, as evolutions of its original meaning. Quantum and inflationary
additions to the celebrated singularity theorems by Penrose, Geroch, Hawking
and others led to subsequent results by Borde, Guth and Vilenkin. And
corresponding corrections to the Einstein field equations have originated, in
particular, $R^2$, $f(R)$, and scalar-tensor gravities, giving rise to a
plethora of new singularities. For completeness, an updated table with a
classification of the same is given.
