Consider a flat Robertson-Walker metric. When we say that there is a singularity at $$t=0$$ Clearly it is a coordinate dependent statement. So it is a "candidate" singularity. In principle there is "another coordinate system" in which the corresponding metric has no singularity as we approach that point in the manifold. However, we know that Big Bang is "a true" singularity, but how should we test that? Is it intuitively self-evident, or should we check rigorously all scalars based on the Ricci tensor? If so "which order of scalar" goes to infinity at that point called Big Bang?