# 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
• – user4552 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
• – user4552 Dec 14 '18 at 22:31
• Naked singularities are generally defined in a way that specifically excludes the big bang, since it is considered one of the acceptable kind of singularities – Slereah Apr 10 at 10:53