favoured topology of Universe candidates

[Boud Roukema]

Hi again Ken & Ali,

On Thu, 14 Feb 2002 Kengrimes123 w aol.com wrote:

> Thanks once again for the prompt feedback, which we would like to say was a 
> model in how to suggest quick and concrete improvements (if only more 
> contributors could do that!) We have gone for the simple expedient of 
> incorporating all of them.

Great! Well, I've stoically ;-) learnt that careful, precise criticism
tends to yield better results than general rants!
 
> Please find below our proposed ending (featuring once more your good self - 
> and if you don't like the phrase 'quiet stoicism' we can go for 'cheerful 
> resignation' instead). We'd be very grateful if you could check this quickly, 
> as I think it probably repeats the 'howler' you picked out in your Point 5:


> ' ... "If the universe is relatively large compared to its age,'
> Levin observes, "I.e if it is significantly bigger than about 15
> billion light years across, then light from our ghost images will
> not have time to reach us before the death of this planet."

OK.
 
> So the universe may indeed be finite and bounded, and yet too vast to yield 
> to us the secret of its shape. 

OK.

> Alternatively, the universe may possess 
> hyperbolic curvature, and so hide its secret shape among limitless 
> possibilities.  

Hmm. Even though there are limitless possibilities for both the spherical
and hyperbolic cases, as far as analysis of MAP data is concerned, 
the difference between them and the flat cases is "just" a question of
calculation techniques and computer speeds. ("just" means a lot of hard
work...) As you said in your article, Cornish et al. will calculate
the easier cases first, simply because they're easier.

The "limitless" or difficult classification of hyperbolic spaces just
means it's much harder to analyse the data - the matched circles principle
of Cornish, Spergel & Starkman is still perfectly valid.

Just a reminder:
the smallest "size" of the Universe could be:
i)  smaller than the horizon size (distance to last scattering surface)
ii) about the same as the horizon (still maybe detectable)
iii) much bigger than the horizon
iv) infinite

(There are in fact several "sizes" of the Universe which could be 
defined, the smallest one is the smallest distance between two images
of the same object.)

the curvature of the Universe can be:
a) "slightly" spherical (like the Earth is "slightly" spherical)
b) flat
c) "slightly" hyperbolic 

There *is* some link between the two, 
[ a) => maximum size of Universe; b) => minimum size of Universe]
but I think it's too subtle to include in your article, certainly too
subtle for a conclusion.

I think probably the closest correct thing to what you want to say
is to compare the three possibilities:
i) + ii)  (put together)
iii)
iv) 

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So here's my suggestion, to replace:

> Alternatively, the universe may possess 
> hyperbolic curvature, and so hide its secret shape among limitless 
> possibilities.  

by

% Alternatively, the universe may really be infinite and unbounded,
% leaving us without the merest hope of being able to distinguish 
% between the two cases.
----------------------------------------------------------------------

> Such thoughts are met with quiet stoicism by the new wave of
> cosmologists: "The universe is however it is," Roukema acknowledges,
> "Not how I would like it to be."

"quiet stoicism" and your quote are fine. :-)

 
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> But there remains the tantalising third possibility - that the universe is 
> neither vast nor hyperbolic. In that case, within a few months of reading 

To match the above correction:

% neither vast nor infinite. In that case, within a few months of reading 
----------------------------------------------------------------------


> this article, we might well know whether Homer's donut is truly the shape of 
> things to come.'

Cheers
Boud