B Questions about the Timeline of the Big Bang

  • Thread starter Cerenkov
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One more thing, Peter.

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."


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.


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.
 
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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.
No, it means that they found it difficult to imagine the possibility that the presence of a positive cosmological constant would actually prevent a singularity from forming. In other words, they did the following:

(1) They proved, mathematically, that if the energy conditions were true, an expanding universe like ours would have to have a past singularity.

(2) They conjectured that if a positive cosmological constant were present, which means the energy conditions would not be true, an expanding universe would still have a past singularity, because they found it difficult to imagine that just the presence of a positive cosmological constant would be enough of a change from the conditions to which their theorem applied that it would prevent a singularity from forming.

Quite honestly, I find it difficult to imagine how they found it difficult to imagine that a positive cosmological constant would make a difference, since the simplest known solution with a positive cosmological constant, namely de Sitter spacetime, has no singularity anywhere. Which seems to me to be an obvious clue that the presence of a positive cosmological constant does make a big difference.

when a positive cosmological constant was indicated by the 1998 data it meant that the theorem could not be directly applied
That's correct. But it doesn't mean their conjecture about what would happen with a positive cosmological constant could not be applied. If it does turn out that our actual universe does not have a past singularity, which is an open possibility at this point, then their conjecture (as opposed to their singularity theorem, which is perfectly valid as a mathematical theorem) will simply be wrong. Not inapplicable, but wrong.
 
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Thank you for your clarification and correction, Peter.

One last question, if I may.

Since it's the energy condition of the H - P theory that would necessarily be violated by a positive cosmological constant, is that what Hawking and Penrose were referring to in the Introduction, in the first of the four physical assumptions?

"(i) Einstein’s equations hold (with zero or negative cosmological constant), "

Thank you.

Cerenkov.
 
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is that what Hawking and Penrose were referring to in the Introduction, in the first of the four physical assumptions?
In the parenthetical comment, yes--a zero or negative cosmological constant does not violate the relevant energy conditions, but a positive cosmological constant does.
 
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In the parenthetical comment, yes--a zero or negative cosmological constant does not violate the relevant energy conditions, but a positive cosmological constant does.
Thank you Peter.

As a result of our dialogue I'm currently reading this paper. https://arxiv.org/pdf/gr-qc/0001099.pdf Energy Conditions and their Cosmological Implications

It looks like I may well have further questions about the SEC. If that's so, then should I post them here, as a continuation of this thread, or begin a new one? I'll go with whatever you recommend.

Thanks again.

Cerenkov.
 
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It looks like I may well have further questions about the SEC. If that's so, then should I post them here, as a continuation of this thread, or begin a new one?
Please start a new thread. If it's a general question about energy conditions, not particular to cosmology, it should probably be in the relativity forum instead of this one. For example, questions arising from the paper you linked to would fall into this category.
 

phinds

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Whew! Gentlemen, thank you.... that helped. For a minute there I was beginning to imagine giant caterpillars smoking hookas might be real ;)
They ARE real. Just not in our universe :smile:
 
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Please start a new thread. If it's a general question about energy conditions, not particular to cosmology, it should probably be in the relativity forum instead of this one. For example, questions arising from the paper you linked to would fall into this category.
Thank you for the advice Peter. I'll do just that.

Cheers.

Cerenkov.
 

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