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I've just been re-checking the 1970 singularity paper by Hawking and Penrose and noticed this.

*"In this paper we establish a new theorem, which, with two reservations, effectively incorporates all of I, II, III, IV and V while avoiding each of the above objections. In its physical implications, our theorem falls short of completely superseding these previous results only in the following two main respects. In the first instance we shall require the non-existence of closed time like curves. Theorem II (and II alone) did not require such an assumption.*

Secondly, in common with II, III, IV and V, we shall require the slightly stronger energy condition given in (3.4), than that used in I. This means that our theorem cannot be directly applied when a positive cosmological constant Lambda is present. However, in a collapse, or ‘ big bang’, situation we expect large curvatures to occur, and the larger the curvatures present the smaller is the significance of the value of Lambda. Thus, it is hard to imagine that the value of Lambda should qualitatively affect the singularity discussion, except in regions where curvatures are still small enough to be comparable with Lambda."

Secondly, in common with II, III, IV and V, we shall require the slightly stronger energy condition given in (3.4), than that used in I. This means that our theorem cannot be directly applied when a positive cosmological constant Lambda is present. However, in a collapse, or ‘ big bang’, situation we expect large curvatures to occur, and the larger the curvatures present the smaller is the significance of the value of Lambda. Thus, it is hard to imagine that the value of Lambda should qualitatively affect the singularity discussion, except in regions where curvatures are still small enough to be comparable with Lambda."

Now, I read this to mean that Hawking and Penrose anticipated the possibility of a positive cosmological constant, but found it difficult to imagine that our universe would actually display such a thing.

### Cosmological constant - Wikipedia

en.wikipedia.org

So, when a positive cosmological constant was indicated by the 1998 data it meant that the theorem could not be directly applied.

How is my reading of this extract?

Thank you.

Cerenkov.