# Is the Big Bang a naked spacelike singularity?

While reading some answers on similar topics, I was wondering about the nature of the Big Bang singularity in the standard cosmological model. I know it's a spacelike singularity that have a causality horizon, but I have read several contradicting answers and comments about it being "naked" or not (I admit that I may have contributed myself to the confusion!). So my question is this :

Is the Big Bang a naked singularity in the standard cosmological model?

In a flat space ($$k = 0$$) dust universe, the causality or particles horizon (NOT the same as event horizon) is located at a proper distance $$\mathcal{D}_{\mathcal{C}}^{\text{dust}}(t_0) = 3 \, t_0$$, where $$t_0$$ is the age of the dust universe. The scale factor is $$a(t) \propto t^{\frac{2}{3}}$$. Thus, a comoving observer cannot "see" what's on the other side of this horizon, until he waits for a time $$t > t_0$$. There is no event horizon in this spacetime. So is the Big Bang singularity at $$t = 0$$ clothed or naked?

• If your definition of naked is that things can escape to infinity then yes, since everything you see came from the Big Bang. – Javier Dec 14 '18 at 15:18
• – Ben Crowell Dec 14 '18 at 15:21
• @Javier, this is how I was considering the Big Bang singularity. But according to Ben (answer below) and Penrose's defintion, it isn't naked. I understand that the answer depends on the definition, but I feel unsatisfied by Penrose's definition. – Cham Dec 14 '18 at 15:58
• – Ben Crowell Dec 14 '18 at 22:31

The big bang is certainly spacelike. If you use the definition in Penrose 1973, then the big bang is not a naked singularity. See pp. 85-86 of that paper. He defines a naked singularity as one that can be in both the past and future light cones of the same observer. He describes how this is specifically formulated so that the big bang is not a counterexample to cosmic censorship.

Penrose, Gravitational radiation and gravitational collapse; Proceedings of the Symposium, Warsaw, 1973. Dordrecht, D. Reidel Publishing Co. pp. 82-91, http://adsabs.harvard.edu/full/1974IAUS...64...82P (not paywalled)

• So is the Big Bang a "clothed" singularity? Can it be both non-clothed and non-naked, like any regular event in spacetime? – Cham Dec 14 '18 at 15:43
• @Cham: I'm just stating Penrose's definition and applying it. There's no way to answer the questions in your comment unless you define terms like "clothed." like any regular event in spacetime? No, a singularity is not an event. – Ben Crowell Dec 14 '18 at 20:25
• Of course, I know that a singularity isn't an event. I was just pointing that usual "regular" events don't have any horizon, and thus aren't "clothed" (by an horizon) and aren't "naked" neither. – Cham Dec 14 '18 at 22:24