# Is Penrose's CCC consistent with Penrose's singularity theorem?

According to Penrose's Conformal Cyclic Cosmology (CCC), there were universes prior to ours, prior to the singularity of our universe.

But how is this claim compatible with his famous singularity theorem, according to which spacetime geodesics cannot be extended beyond a singularity?

I believe Penrose doesn't deny the big bang singularity. Then how does he make sense of 'spacetime prior to the big bang singularity' in CCC?

• Since CCC only identifies timelike infinities, I dont think there is a problem with geodesics passing singularities. Oct 31 '20 at 18:24

My reading of the paper is that there is a singularity, in the sense of the singularity theorems, at the beginning of each cycle, but it's physically irrelevant because physics is precisely scale invariant there. The FLRW metric in terms of conformal time is $$ds^2 = a(η)^2 (dη^2 - d\mathbf Σ^2)$$, where the "coordinate" $$\mathbf Σ$$ ranges over a sphere*. If the scale factor is physically irrelevant then the space is effectively a sphere at the big bang even though $$a(η)\to 0$$. (In particular see the top half of the left column of page 2761.)