favoured topology of Universe candidates

[Boud Roukema]

Hi again Ken & Ali,

On Thu, 14 Feb 2002 Kengrimes123 w aol.com wrote:
> Thanks for that. We were rather shamefully going for the following 'quick 
> fix.' What do you think:

The problem is that a spherical or hyperbolic, small universe would be
just as exciting as a flat, small universe. The former might be more
difficult to imagine, and there's more chance that Cornish et al would
make errors or miss the real signal or take longer to find the result
for a spherical or hyperbolic small universe than for a small, flat
universe, but to me that's a secondary issue. (Using the circles
principle in the most general way, the infinities of possibilities are
not a problem for detection, however paradoxical that might seem!)

Nevertheless, if what you really want to say is that a flat, small
universe is in some ways "nicer" or "simpler" than a spherical or
hyperbolic, small universe, then that is valid (and certainly
defendable), but should probably be worded a bit more carefully.

It would not really be that much more "hidden" from the measurement
point of view, it would be more hidden simply because it's more
complicated. 

I think the following is correct, clear and probably close to what you
want to say:

Replace:

> 'So the universe may indeed be finite and bounded, and yet too vast to yield 
> to us the secret of its shape. Alternatively, the universe may possess 
> spherical or hyperbolic curvature, and so hide its secret shape among 
> limitless possibilities.  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."

by 

% 'So the universe may indeed be finite, bounded and flat,
% and yet too vast to yield 
% to us the secret of its shape. Alternatively, the universe may be 
% small but possess 
% spherical or hyperbolic curvature, and so hide its secret shape among 
% limitless possibilities difficult for ordinary mortals to imagine 
% and challenging for professional
% cosmologists to extract from the MAP data.  Such thoughts ...

And then the 2nd paragraph is fine unchanged:

> But there remains the tantalising third possibility - that the universe is 
> relatively small, and possesses flat curvature. 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