Dear Ken & Alison, I would be pleased for my scientific work to be featured in the article. :)

I don't know how much you would like me to write and how much you would like to rewrite yourselves. But I think it's in the interests of non-scientists' right to "eavesdrop on science" for me to give you more detail, including published references, than you are likely to want to publish. If you wade through the articles and come out feeling dizzy, please feel free to ask more questions and I'll try to help clarify things.

Even so, I'm not convinced that my initial response explains enough for the lay reader, but it's already rather long as it stands, so have a read through and tell me where you want to go from here.

* General reading: I would strongly recommend that you read my BASI review

http://uk.arXiv.org/abs/astro-ph/0010185

which should be quite accessible to science journalists and give you my version of how the different approaches relate to one another.

* Affiliation: By the time your article is published, my affiliation will be Torun Centre for Astrophysics, University of Nicolas Copernicus, Torun

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1. Which (if any) of the current candidates for the topology of the universe

do you favour, and why?

1a) which candidates do "I favour" ? 1b) why?

---------------------------------------------------------------------- 1a) which candidates do "I favour" ?

Well, the verb "to favour" is really about my personal pyschological reactions, which only weakly correlate to scientific reality!

But I can tell you the three candidates, in chronological order, for which I think observational predictions should be tested, as well as the intuitive, subjective probabilities which I've tried to assign to their being correct - since you asked! If that's what you mean by "favour", fine.

(1) "three cluster identity": Coma cluster/RX J1347.5-1145/CL09104+4109 model class: 2-torus comoving size of Universe: about 1 h^{-1}Gpc (Hubble constant = 100h km/s/Mpc) subjective probability: 10%

references: - Serendipitous discovery in discussion of clusters seen in X-rays http://uk.arXiv.org/abs/astro-ph/9706166 Roukema & Edge - optical analysis from archival data http://uk.arXiv.org/abs/astro-ph/9903038 Roukema & Bajtlik - COBE cosmic microwave background (CMB) analysis (assumes cosmological constant=0) http://uk.arXiv.org/abs/astro-ph/9910272 Roukema

(2) "COBE counterexample" model class: 2-torus comoving size of Universe: about 2 h^{-1} Gigaparsec or greater subjective probability: 20%

references: - COBE cosmic microwave background (CMB) analysis http://uk.arXiv.org/abs/astro-ph/0007140 Roukema

(3) "radio galaxy pair": identity of radio-loud active galaxies 3C186/4C+36.21 model class: only one generator hypothesised comoving size of Universe: about 1 h^{-1} Gigaparsec subjective probability: 10%

references: http://uk.arXiv.org/abs/astro-ph/0111052 Roukema, Marecki, Bajtlik, Spencer

---------------------------------------------------------------------- 1b) why?

Probably my true answer for (1)-(3) is: because they haven't been falsified yet. (A technical note: (1) was falsified in astro-ph/9910272 under the assumption of zero cosmological constant, which was still a reasonable assumption at the time the work was done, in 1998, but it is now clearly a bad assumption, so (1) is again a valid candidate.)

As for the values of my subjective probabilities, well, they're subjective. I did happen to notice after writing them down that:

P(subjective)= 10% size of Universe in h^{-1}Gpc

but this is not a true description of my personal psychological state, since I would not give a 100% probability to a model 10h^{-1}Gpc in size! ----------------------------------------------------------------------

2. What research methods are you (and others sharing your view) following,

and what progress is being made?

(1) "three cluster identity".

This candidate makes predictions that it should be possible to point a telescope at certain angular positions in the sky and detect clusters at certain distances (redshifts). If a cluster is found at the correct position and redshift, the hypothesis would be strengthened. If it were definite that no cluster existed at the predicted position and redshift, the hypothesis would be falsified.

With my colleagues Jean-Michel Alimi, Jean-Pierre Luminet, Dominique Proust, (LUTH & GPI, Observatoire de Paris-Meudon), Stanislaw Bajtlik (Nicolas Copernicus Astronomical Centre, Warsaw) and Etienne Pointecouteau (Tohoku University, Japan), various requests for observing time on optical telescopes have been made. We had some service time allotted in 2001 on the Anglo-Australian Telescope, in principle, but the schedule did not allow observations to be made. We will continue this programme of optical telescope tests.

(Note: members of the group differ on the subjective probabilities they assign to the candidate being the right one!)

(2) "COBE counterexample"

Although this is the candidate I'm probably the most interested in, it's also the hardest to test, because the larger scale implies that multiple images ("topological lensed images") of ordinary astrophysical objects exist at high redshifts, meaning long lookback times into the past history of the Universe, so that not only is it most difficult to observe the high redshift images (because they are faint!), it's also likely that the objects didn't exist yet at that early epoch.

The MAP and Planck satellites will probably provide the best tests of this hypothesis, though making a correct analysis with as few as possible theoretical assumptions is likely to be fiendishly difficult. As far as I know (but science history is not my field!), Geoffrey Marcy and Paul Butler missed the detections of exoplanets in their own data in the early 1990's because they had accepted the theorists' "reasonable" assumption that massive planets (Jupiters) could not exist in short period orbits. Such "reasonable" assumptions for detecting cosmic topology might also lead to a discovery remaining hidden for many years...

(3) "radio galaxy pair":

Although the morphologies (shapes) of these two radio galaxy jets are strikingly similar, the redshift (equivalently, cosmological epoch when the light was emitted) of only one of them is known. Radio galaxy jets expand at very high speeds, from 1% to over 100% (in apparent speed) of the speed of light.

So, the hypothesis can only be valid if the redshift - and the cosmological time of emission of the light making the image - of 4C+36.21 is just slightly higher - cosmological time slightly earlier - than for 3C186. The prediction for the redshift of 4C+36.21 is 1.0630 < z < 1.0635.

A redshift measurement will either strengthen the hypothesis, or falsify it.

My colleague Andrzej Marecki (Torun Centre for Astrophysics, University of Nicolas Copernicus, Torun) has time on the William Herschel Telescope in the Canary Islands for a spectroscopic measurement of this redshift, so we hope to have an answer in the coming year!

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From: Kengrimes123@aol.com Date: Mon, 07 Jan 2002 13:18:13 -0500 (EST) Subject: Astronomy magazine article. To: boud@iucaa.ernet.in

Dear Dr Roukema

We are two science journalists currently writing an article for Astronomy magazine (a US title with a circulation of approximately 300,000 readers). The subject of the article is hyperspace and the topology of the universe, and we wonder if you would be interested in being featured in the article.

The issues we are concerned with are:

1. Which (if any) of the current candidates for the topology of the universe

do you favour, and why? 2) What research methods are you (and others sharing your view) following, and what progress is being made?

We can be contacted at this return e-mail address (kengrimes123@aol.com). Should you prefer to speak via telephone, please let us know what would be a suitable time to call you.

Email is fine.

Many thanks for you attention,

Ken Grimes & Alison Boyle.

Glad to be of help,

Boud Roukema

boud@astro.uni.torun.pl Torun Centre for Astrophysics, University of Nicolas Copernicus, Torun http://www.astro.uni.torun.pl/ (affiliation by the time the article is published!)