Cosmo-torun January 2002

cosmo-torun@cosmo.torun.pl

5 participants
7 discussions

Updated programme!
by Andrzej Marecki 21 Jan '02

21 Jan '02

Updated programme! == Cosmo-Torun Mini-Workshop 14:00, Wed 23 Jan 2002 TCfA == Welcome to the Cosmo-Torun Mini-Workshop. This is intended to help us start to learn about each others' interests in cosmology and how we can carry out research together. Please feel free to invite anyone likely to be interested, and help them to access the page containing this document! Background reading of http links is not compulsory but would obviously help. Date: Wed 23 Jan 2002, time: 14:00-17:30 Proposed programme, including links to background reading: 14:00-14:30 (5 mins presentation, 25 mins qns, discussion) Michał Frąckowiak - A few words about quintessence 14:30-15:00 (5 mins presentation, 25 mins qns, discussion) Sebastian Soberski - A few words about OCRA 15:00-15:30 (5 mins presentation, 25 mins qns, discussion) Rafał Kosiński - A few words about cosmic topology 15:30-15:40 coffee/tea break 15:40-16:10 (20 mins presentation, 10 mins qns, discussion) Michał Hanasz - Cosmic rays and magnetic fields - are they relevant for galactic evolution? 16:10-16:40 (25 mins presentation, 5 mins qns, discussion) Andrzej Marecki "How can we use radio-loud AGNs as probes of topology?" http://de.arXiv.org/abs/astro-ph/0201092 16:40-17:00 (20 mins discussion based on points in msg00018.html) discussion of the cosmo-torun list and related mailing lists http://www.astro.uni.torun.pl/sympa/cosmo-torun/2001-12/msg00018.html 17:00-17:30 (15 mins presentation, 15 mins qns, discussion) Boud Roukema "A Cosmic Standard Ruler" http://de.arXiv.org/abs/astro-ph/0106135 --------------------- See: http://www.astro.uni.torun.pl/sympa/cosmo-torun/2002-01/thrd1.html to find out more. -- Andrzej

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spotkania cosmo-torun 21-25 stycnia?
by Boud Roukema 18 Jan '02

18 Jan '02

Cze�� wszystko, Proponuj� wizyt� w Piwnice 21-25 stycznia, i spotkania cosmo-torun. Co my�lecie? My guess is that a one-hour meeting would be enough, but Andrzej suggested a full afternoon. I would be happy either way, but it only makes sense to do what most people prefer. Could everyone (except Motylek who I presume is in JBO now) say what they would prefer in terms of (i) time length (ii) which time (iii) which topics? I suggest people just write their answers to the list or concatenate them with previous answers. Our numbers are small enough that cut/paste should be enough. (i) 1 hour meeting ? one afternoon 14h-17h30 meeting ? (ii) Mon 21 Tue 22 Wed 23 Thu 24 Fri 25 Which are impossible? preferred? (iii) My idea of an easy cut/paste way to see what people want to talk about. Please put a rating + 0 - in front of the following topics (or concatenate your rating to previous ones). The values are +1, 0, -1 respectively. The final ratings are added up and then we will know which people are most interested in. science ------- + Rafa� - cosmic topology? (Just say something about what you understand, or what your questions are, or why you think we're doing things wrongly, what you think we should do, whatever! This is not an exam: we know you have not published any research papers in the subject, so there's no embarrassment if there are gaps in your knowledge. There are certainly big gaps in my knowledge. Be creative!) + Micha� F - quintessence? Could you teach us something about quintessence, scalar fields in a way that we all understand and can relate to our work? + Sebastien - something about OCRA? What you are doing, what is planned, the time schedule. How the scientific use of the data is planned (this is in fact partly a political question, which you should probably discuss with Andrzej Kus - maybe Andrzej K could come along and let us know what the ideas for this are so that nobody gets upset by us suggesting analysis plans against the wishes of the people running the project!) 0 Andrzej M - non-topology work or topology work, as you like - Micha� H - something about your AGN work - Boud - cosmic topology; cosmic standard ruler; or galaxy formation meta-discussion --------------- + discussion of the cosmo-torun list, what do people think of creation of the other spinoff lists I've suggested (listed below) or which others may suggest, in particular, the idea of a list dedicated to each project or article? 0 development of cosmo-torun web pages - is anything needed yet? Ideas for spinoff lists: ------------- * cosmo-seminar: For organising meetings (whatever the title, "journal club", "seminar", "workshop", "conference") in Toru� and/or Warsaw and/or other Polish cities (e.g. there's a theoretical cosmo group in Krak�w). I suggest no access restrictions, since no "unpublished research ideas" are likely to be posted here. * cosmo-pl: For general discussion, organisational, scientific, whatever, among Polish cosmologists and extragalacticians. Again, no access restrictions. * topo-rlagn: [cosmic topology radio-loud AGN projects] * ocra: Sebastian Sober ? * shape-univ: I've offered to Andrzej Woszczyk and said to some students that I would be happy to teach a "monograph course" on observational constraints on the shape of the Universe (curvature + topology) during the next semester (which I believe starts 18th Feb 2002). * other Are there any existing lists? Someone told me something about a list called astronomia(a)astri.uni.torun.pl . It seems to me one list which could be useful (for publicity purposes) would be one for discussing TCfA web pages. It's not always obvious what changes are good ones, and it's a lot of pressure on the webmaster if he/she alone has to decide to accept/reject suggestions/requests. A mailing list would make the decisions more collective. Pozdrawiam, Boud Summary: These are the questions which it would be good to answer or give a rating to (respectively) in order that the meeting can be in the best interests of everybody! Just cut, paste and edit! ====================================================================== -- cut ---- cut ---- cut ---- cut ---- cut ---- cut ---- cut ---- cut -- ====================================================================== (i) 1 hour meeting ? one afternoon 14h-17h30 meeting ? (ii) Mon 21 Tue 22 Wed 23 Thu 24 Fri 25 Which are impossible? preferred? (iii) Please add + 0 - to the beginning of each line. You can add other lines for discussion if you wish! + Rafa� - cosmic topology? (Just say something about what you + Micha� F - quintessence? Could you teach us something about quintessence, + Sebastien - something about OCRA? What you are doing, what is planned, 0 Andrzej M - non-topology work or topology work, as you like - Micha� H - something about your AGN work - Boud - cosmic topology; cosmic standard ruler; or galaxy formation + discussion of the cosmo-torun list, what do people think of creation 0 development of cosmo-torun web pages - is anything needed yet? ======================================================================

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Re: favoured topology of Universe candidates
by Boud Roukema 13 Jan '02

13 Jan '02

Hi, just an explanation for the discussion with the media people. I think it's useful to cross-post this (1) so that in case the journalists publish wrong or misleading statements, there are at least some colleagues who know what my version of the story was; (2) it's probably useful for everyone since it's a discussion at a very pedagogical level, and should help to make it clear to everyone that I'm not a "believer" in any of the hypotheses I work on. If there's a lot of this, I would prefer to spin this off into a completely open list, e.g. cosmo-torun-media , so that anyone interested could read it. Cze�� Boud

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Re: favoured topology of Universe candidates
by Boud Roukema 13 Jan '02

13 Jan '02

Dear Ken & Alison, Glad you're getting back to me for feedback. This is definitely a good way to check we understand each other. :-) > Date: Sat, 12 Jan 2002 14:28:52 EST > Subject: Re: favoured topology of Universe candidates > To: boud(a)astro.uni.torun.pl > Dear Boud, > > Many thanks for your prompt reply. We have read through your e-mail and BASI > review, and would like to check that we have understood correctly (not being > experts in this field). > > We understand that you are researching possible shapes of the universe which > are finite, unbounded, and multiply connected (such as a hypersphere, > 3-torus, 3-Klein Bottle or other 4D polyhedra). This would imply that we are OK, two comments. (a) science Correct, except that I'm also researching possible *infinite*, unbounded, and multiply connected models. A finite model would be more aesthetically pleasing, but it is best to do observational work with as few prior hypotheses as possible. The Universe is how ever it is, not how I would like it to be. (b) pedagogical, terminology The "shapes" such as the hypersphere, the 3-torus, the 3-Klein Bottle are *not* "4D polyhedra". Technically, they are called "3-manifolds", but since that is rather scary to non-specialists (including many astronomers!), a more friendly term would be "3-spaces" or "3-dimensional spaces" - which can be thought of with the *help* of a 4th dimension - or which can be thought of as 3D polyhedra where certain faces are identified in some way. It is *very* important to explain that when a 4th dimension is used to help think about a 3-space, this is purely a psychological tool, a mental crutch for human beings having difficulties thinking in a multiply connected and/or curved 3-space, simply because we are biased from our childhood experiences and school education to think in terms of Euclidean, simply connected 3-space. It might sound like gestalt psychotherapy ;-) to say this, but as far as a mathematician or physicist is concerned, a 3-dimensional space exists in and of itself, it has no need for the existence of extra dimensions to be itself, even if an extra dimension or too helps it (or beings living inside it!) to understand what it is. In "brane theory", it is true that 4th & 5th dimensions are thought of as true physical dimensions, but the field of observational studies of the topology of the Universe is separate from brane theory. But then again, the 4-dimensional or 5-dimensional models could again be thought of in spaces with an extra "psychological" dimension of no physical meaning, i.e. 5D or 6D spaces, again with the extra dimension just as a thinking aid. So I think the issue of a dimension as a thinking aid with no physical meaning cannot be avoided. I would recommend that in your article you explain something of this issue - the fact that as far as most observational cosmologists interested in either curvature and/or topology are concerned, a 4th dimension is a useful psychological tool for thinking, but is used without any physical meaning. If we go one dimension down, to make things easier, I can refer to Figure 1 of my BASI article http://uk.arXiv.org/abs/astro-ph/0010185 . Here I discuss a 2-space, the "2-torus". There are three different ways (i)-(iii) of thinking about the same space. It's a good exercise to try switching between the three ways and checking that you can understand them as the same thing. In (i) (lower figure), I use ordinary 3-space to help the reader imagine what the 2-space is. In (ii) and (iii), the reader does not need to think at all in 3-space. 2-space is enough, even though it may seem a little weird. Going back up a dimension, it is possible to imagine various 3-spaces, either like (i) within a 4-space or like (ii) and (iii) just within ordinary 3-space, but a little weird. > seeing repeated copies of a small universe (rather than a single very large > or infinite one). Your research centres around studying the sky to identify > repeated patterns of objects (celestial bodies and/or temperature signatures > in the microwave sky) to infer a size and shape for this "tiled" universe. Correct. For more clarity, you might want to put "...studying the sky in three dimensions to identify..." BTW, when you say "tiled" Universe, you're referring to mode (iii) of thinking. > Presumably, in order to decide in which directions, and at which distances, > to look for these repetitions, you must be working from a hypothesis about > the possible shape. For example, according to John Gribbin's New Scientist > article from that date, in 1997 you seemed to be looking for quasar patterns > to support a "twisted torus" or "3-Klein bottle" hypothesis. Nope. I'm a skeptical observer who works the other way around! There is no serious theory for the extension of general relativity which would give a theory of global geometry, and even if there was, the best bet would still be to make observations with as few preconceived ideas as possible. The standard Big Bang model, by the way, is a preconceived idea which I and my colleagues *do* assume, since it (and the theory of general relativity) is (are) extremely well established observationally. Rather than working from a specific hypothesis about the shape, my general approach is on finding the best ways of using existing (or near future) observational data catalogues. It happens that during some of these projects, serendipitous candidate topologies have turned up. I think all of (1), (2) and (3) that I gave you in the previous message are best described as serendipitous, though (2) comes from a (slightly) more systematic approach than (1) and (3). The candidate from my John Gribbin article was found using a very systematic approach, but at the moment it is just sitting in my "list-of-things-to-do". Although it was found systematically, I would probably class its "subjective probability" as 5%. But my subjective probabilities are... subjective. The only serious way to check candidates is by further observational work. BTW, the implicit 3-Klein-bottle-like model was what the observations gave, not what I was looking for. I would have preferred to find a 3-torus than a 3-Klein-bottle-like model! > Your e-mail suggests that your current research focuses on the use of galaxy > clusters and microwave patterns to identify a "model class: 2-torus". Are we Hmmm. I don't know if the following is too subtle for a general audience. See how you like it. I would prefer to say: ---- My current research focuses on the use of galaxy clusters and microwave patterns in which serendipitously discovered 2-torus models offer good prospects of observational tests. Later on, if more complicated models are offered as candidates, the experience in testing 2-torus models will be important for testing the more complicated models. After all, if it is not possible to observationally test a 2-torus model, which is relatively simple, how could we possibly hope to test a more complicated model? Candidate (3) is even less ambitious: it involves just one generator, or path between two images of (hypothetically) the same object. ---- [plus a modification of the term "2-torus" as per the comment below] > right in assuming that this refers to an actual universe in the shape of a > (non-twisted?) 4D 3-torus, which is modelled as a 3D 2-torus? OK, I used an abbreviation without explaining it, sorry! Firstly, as I explained above, the 3-torus is really 3D, and the 2-torus is really 2D, even if an extra dimension is used as a psychological crutch. The model I've called "2-torus" for my observational work on the real Universe (as opposed to pedagogical explanations with one dimension subtracted) is really the 3-torus, but one side length is considered bigger than the horizon diameter, so big that observations made that far away would require the light to have been emitted before the Universe was born. If you called it a "3-torus with one very long side" or a "3-torus with one presumably infinite side length" that would be correct, would probably help avoid confusing readers, and would avoid experts in the field getting confused about what I'm doing. > We would also be interested in your views on other possible tessellated > polyhedra models. In particular, we are interested in any topologies which Well, again, I would prefer to say "other possible 3-spaces" or "other possible, multiply connected 3-spaces, which can be thought of as tesselated polyhedra models". > may be consistent with the recently emerging field of braneworlds. For > example, Michael R. Feltz's website - http://www.cyburban.com/~mrf/ - > identifies brane theory with the Riemannian hypersphere topology. Well, I quite like the idea of non-experts writing web pages (if I hadn't been job-hunting for the past few years I probably would have made more effort to interact with non-specialists, and maybe sometime in the future I will be able to...), but I'm afraid there is some confusion in Michael Feltz's page: : The discussion here attempts to answer this question as it relates to : the often hypothesized, but little explored, "finite but unbounded" : universe. The formal name for this model in topology and cosmology is : a "closed cosmic hypersphere". There are many finite but unbounded models other than the hypersphere, e.g. the 3-torus. : Otherwise the days of an expanding universe are numbered because this : high density model will expand only to certain maximum size and then : contract into a "big crunch" ("big bang" in reverse) at some future : date at least tens of billions of years from today. Correct. And the geometry of *this* model is a 3-sphere, also known as a hypersphere. : The alternate model explored in this series of essays is the long : suspected and often hypothesized "closed cosmic hypersphere" which : incorporates a fourth spatial dimension. The hypersphere provides one of the three possible curvatures, plus the assumption of trivial topology. Calling it the "closed cosmic hypersphere" is OK. But it does *not* incorporate a fourth spatial dimension. A fourth, psychological, dimension is just one possible way to think about it. And it is not an "alternate" model. It is the model which (for reasonable values of the local cosmological parameters, which show that the Universe is "approximately" flat, like any continent on the Earth is "approximately" flat) will expand to a maximum size and then contract into a "big crunch". Back to your question! My views on other possible "tesselated polyhedra" models (and now you know they're physically only 3D, not 4D), are that I'm totally open to any of these multiply connected models, whether for a flat Universe (where the angles of a triangle add up to 180�, and this includes the "3-torus with a very long side" models - this is a flat model!), for a spherical Universe ("hypersphere", where the angles of a triangle add up to more than 180�) or for a "saddle-shape" Universe ("hyperbolic", where than angles of a triangle add up to *less* than 180�). Of course, in either the spherical or the saddle-shape cases, the observable part of the Universe would be approximately flat, again like any continent on the Earth is approximately flat. > Given that the readers of Astronomy are mainly non-scientists, we would be > very grateful if you could provide as simple an explanation as possible. I know very little about brane-theory, but I think it is still much too theoretical to have any serious links with observational work. I think the best link you could make between observational cosmic topology work and brane theory could be something like the following: ---- Scientists trying to measure the 3-dimensional shape of space (with a type of non-expanding map of the Universe called "comoving" - although in reality the Universe is expanding, in this special map, the Universe can be thought of as static) sometimes use a psychological 4th dimension to explain or think about different possibilities for the shape of space, e.g. a 3-space which seems to be tesselated by many copies of the Universe. Other, more theoretical scientists, working on "brane theory", think that 4th and 5th dimensions might have real physical meaning (of course, there's also time, making a 6-dimensional world). However, the scientists trying to measure the 3-dimensional shape of space (also called the topology and curvature of space) prefer a more conservative, purely empirical approach and would like to measure the shape of 3-space without any preconceived notions, apart from the standard Big Bang model. They hope to detect any of many possible shapes of 3-space, whether it's the 3-torus with one very long side or any other. ---- For more on brane theory, you might want to ask Nathalie.Deruelle(a)obspm.fr, who gave a very nice explanation during a workshop in Paris last year, but unfortunately I was too tired and stressed to really listen properly :-(, though she did seem to give a good explanation. She's definitely an expert in brane theory, and is very supportive of work in cosmic topology. And she's probably one of the best people around who can make an intelligent comment on whether there's any link between the two. > Many thanks once again for your help, My pleasure :-) - feel free to keep passing draft texts to me for comment and/or other questions. Boud boud(a)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!)

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An AGN HR diagram? astro-ph/0201089
by Boud Roukema 11 Jan '02

11 Jan '02

A key to understanding AGN? Proceedings by Peter Barthel from Gr�ningen: "An AGN Hertzsprung-Russell Diagram" http://de.arXiv.org/abs/astro-ph/0201089 Motylek, Andrzej, Micha�, any thoughts?

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favoured topology of Universe candidates
by Boud Roukema 09 Jan '02

09 Jan '02

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 ---------------------------------------------------------------------- > 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! ---------------------------------------------------------------------- > From: Kengrimes123(a)aol.com > Date: Mon, 07 Jan 2002 13:18:13 -0500 (EST) > Subject: Astronomy magazine article. > To: boud(a)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(a)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(a)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!)

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Do Type Ia Supernovae prove Lambda > 0 ?
by Andrzej Marecki 04 Jan '02

04 Jan '02

Paper: astro-ph/0201034 From: M.Rowan-Robinson <m.rrobinson(a)ic.ac.uk> Date: Thu, 3 Jan 2002 16:29:08 GMT (64kb) Title: Do Type Ia Supernovae prove Lambda > 0 ? Authors: Michael Rowan-Robinson Comments: 10 pages, 10 figures. Accepted for publication by MNRAS -- Andrzej

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Cosmo-torun January 2002