hi Aleksandra, [cc: cosmo-media public mailing list]
> wt., 7 mar 2023 o 09:31 Boud Roukema <...> napisał(a):
> > I assume this is your blog: https://medium.com/@szymula.aleksandra
> > You're welcome to ask me some questions - email would probably be the
> > simplest.
> Yes, that is exactly the blog. Thank you very much for giving me this
> opportunity.
>
> These are the questions I'd like to include in this interview:
> 1. For a good start, what is exactly the concept of infinity?
There are many definitions of infinity [1]. The two infinities that
are generally used in practice in cosmology are, informally speaking,
\aleph_0, the amount of natural numbers (counting numbers) [2],
and 2^{\aleph_0}, the amount of real numbers [3]. In simple words,
these two infinities are each the size of a certain set of things.
There's an easy proof of why these two infinities are different,
related to writing down numbers in the decimal system.
[1] https://en.wikipedia.org/wiki/Infinity
[2] https://en.wikipedia.org/wiki/Countable_set
[3] https://en.wikipedia.org/wiki/Cardinality_of_the_continuum
> 2. In your opinion, what is the most mind-bending idea related to the
> infinite universe, and how does it challenge our understanding of the
> nature of existence?
2a. The infinitely repeating identical worlds paradox is fairly mind-bending :).
In a spatially infinite universe, any physical sequence of events with
a tiny probability that is allowed by our known laws of physics would
have a probability of 1 of occurring somewhere. That doesn't mean that
it's certain, just that it's very likely. If the Universe were really
infinite, then it would very likely happen somewhere that a planetary
system almost identical to ours forms, with an Earth almost identical
to ours, and life evolves in almost exactly the same way as it has
evolved here, and the Internet evolves and the Fediverse evolves, just
like these events have taken place here. In some cases, the events
will diverge in a few tiny ways, and gradually diverge more and more.
This must be almost certain (the probability is 1) if the Universe is
really infinite.
You can read some modern descriptions about this paradox
infinite universe in [4] or [5].
2b. Our understanding of the nature of existence is quite limited, so
I don't see the infinitely repeating identical worlds paradox as a
challenge to it. Infinities imply surprising things. It would be a
lot simpler if our Universe were finite - as Ellis & Brundrit mention [4].
[4] Ellis & Brundrit 1979, https://ui.adsabs.harvard.edu/abs/1979QJRAS..20...37E
[5] Garriga & Vilenkin 2001, https://ui.adsabs.harvard.edu/abs/2001PhRvD..64d3511G
> 3. Is the universe infinite in terms of space and time, or is there an
> ultimate boundary?
We don't know if the Universe is infinite or not. So far, we have no significant
evidence of it being finite. In both finite and infinite models of the Universe,
we normally assume that there are no spatial boundaries.
> How does this idea challenge traditional concepts of
> time and space?
The Newtonian cosmological model of infinite space has lots of problems.
General-relativistic models make it a lot easier to have spatially finite
models.
> 4. Can we ever truly comprehend the vastness of the universe?
Unlikely. :)
> And what are some of the most interesting phenomena that suggest its
> infinite nature?
I don't see any evidence of the Universe being infinite. Our current
standard model, if interpreted literally, is of an infinite universe, but
the standard model is not really taken seriously as a complete model - it's
just a fairly good model of all of our observations.
> 5. Now, how do you approach the task of visualizing or representing the
> infinite universe? How has technology aided in our exploration ability?
Either a finite or infinite universe is represented cognitively
through a lot of work using 2-dimensional analogies, drawing diagrams,
making calculations, and developing symbolic mathematical skills and
intuition of differential geometry and of the topology of
3-dimensional manifolds.
My guess is that by "technology" you mean software. The best software for
cosmology is FOSS (free and open source software), since when the software is
*not* free-software-licensed, we're not allowed to understand the software or
correct bugs or improve it. FOSS helps for playing around with calculations,
both with numerical calculations (with numbers) and for symbolic algebra
(SageMath, Maxima).
> 6. There are many theories about how our universe works and all of them
> sound intriguing, as well as confusing. Since there is so many concepts,
> how do various theories of the universe, such as the Big Bang, the parallel
> universe, the multiverse hypothesis, or the concept of fractal universe,
> contribute to our understanding of its infinite nature? How do these
> theories relate to each other?
The Hot Big Bang model is the standard model of the Universe developed to match
general relativity to three observations - the expansion of the Universe, the
cosmic microwave background, and nucleosynthesis - roughly from 1917 to
becoming widely accepted from the 1960s to the early 1990s.
The next level of detail is the LambdaCDM model - roughly from the 1980s to
becoming well accepted by the 2000s. This is currently the standard cosmological
model.
Parallel universes and multiverse models are speculation that are nowhere
near having any observational support.
A fractal structure of the spatial distribution of galaxies is to some degree
a fair approximation on some scales - it's unlikely to change standard cosmology
last time I checked it.
> 7. I mentioned the multiverse universe theory, and I have to say that is
> one of my favorite concepts. Based on that I have to ask, what is the most
> compelling evidence for the multiverse theory, and how does it relate to
> the infinite universe concept?
I don't work on multiverse theory, so I couldn't say. Max Tegmark got quite
famous for this and might want to talk about that. :)
> 8. What implications does the infinite universe have on the search for
> extraterrestrial life?
Completely irrelevant. We're only searching for extraterrestial life
in a finite part of the Universe. The most interesting would be signs of
extraterrestial life within a few parsecs, since in that case two-way
communication within our lifetimes could be possible.
> 9. Can we ever hope to travel to other parts of the universe given its
> infinite nature?
We have no evidence that the Universe is spatially infinite, but even if
we did, that would be irrelevant for space travel.
However, space travel by humans is a low priority. The current
scientific priority is handling the climate emergency [6]. If there
is not too much debris in Low Earth Orbit (LEO) once we get into a
stable maximums of 2 deg C post-industrial warming (I'm being optimistic),
maybe in the 2050s or 2070s or so, then planning on sending some space arks on
multi-decade (or multi-century) journeys to neighbouring stellar
systems *might* become realistic and ethically justified.
[6] https://web.archive.org/web/20230320135908/https://report.ipcc.ch/ar6syr/pd…
> (10). Finally, what is the most promising avenue for exploring the infinite
> universe?
The most interesting thing is looking for evidence that our Universe
is finite, rather than infinite. Space in the standard cosmological
model has both curvature and topology: either positive curvature (like
a 2-sphere) or a multiply connected topology (like a 2-torus) would
be examples where our Universe would be spatially finite. One of the
recently discovered methods of detecting signs of cosmic topology
is topological acceleration [7][8] - by observing the movements of galaxies
carefully enough, we could, in principle, detect signs of the global
shape of the Universe - curvature and topology.
> What do you hope to achieve throughout your research?
It would be great to discover evidence of topological acceleration. :)
However, that's not guaranteed. What is more likely is that the
modelling work and observations and observational analyses needed to
get there will lead to many related, possibly unexpected, side
discoveries in the details of the formation of galaxies and the
structure of the Universe.
[7] https://ui.adsabs.harvard.edu/abs/2007A%2526A...463..861R
[8] https://arxiv.org/abs/2201.09102
All of the above information is public - the latest observational and
theoretical work can all be found on ArXiv [9]. If you see a press
release about a "new" result or idea and there's no corresponding
research paper about it on ArXiv, then it's unlikely to be serious
research.
In principle cosmology can be self-taught - i.e. without attending
university lectures - there's a huge amount of open-access
information. However, in practice, university education is
unavoidable. Good students generally take quite a bit of time (several
years) to work through the standard material. Proposing new
hypotheses in cosmology requires first understanding standard
cosmology.
[9] https://arxiv.org/list/astro-ph.CO/recent
Cheers
Boud

Dzień dobry, [cc cosmo-media mailing list]
Napiszę po angielsku, ale możemy zmienić między językami jak będzie potrzebny.
Apparently you are interested in the article Cyr-Racine et al 2022:
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.201301.
The article presents a rather speculative, but interesting, hypothesis
about mirror matter, offering a possible explanation of the Hubble constant puzzle.
The article starts with a mathematical rescaling aimed at
understanding the relation between the standard cosmological and
observations, and proposes that this purely mathematical exercise could have a
physical interpretation in terms of mirror matter.
The first paragraph on page 201301-3 gives a brief description of "mirror matter",
and how (if it exists) it would relate to ordinary matter.
Figure 1 shows that the authors' mirror matter model would be consistent with
the statistics of Planck observations of the cosmic microwave background.
Figure 2 shows that the model could provide a high value of the Hubble constant,
of about 73 km/s/Mpc, and what the values of other parameters would have to be
for the model to be observationally viable.
* Figure 2 bottom-left and bottom-right show values of parameters of the model
that are most likely not observable.
* Figure 2 top-right shows the value of the helium abundance Y_p that
would be required, and the text (left-hand column of page 201301-4)
gives the numbers involved. The helium abundance is
well-constrained observationally, and the text acknowledges that a bit more
speculation regarding properties of the model is needed in order for
the model to become observationally viable - this is discussed more on page
201301-4. In other words, the model does not quite work, and the authors
suggest future calculations that might help.
Personally, I find a more likely explanation of the Hubble constant
puzzle to be much simpler, related to the fact that the Universe is
inhomogeneous. In terms of real observations, the local part of the
Universe that we observe is necessarily smaller than more distant
parts of the Universe; as a first approximation, this is a simple geometric
effect. Deviations from the average are generally higher in smaller spatial
regions. Our observations (made within our lifetime) necessarily come from
light that passes through our local Universe - which is not quite the
same as an "average" part of the Universe. So deviations on small
scales are not so surprising. The difficulty is doing the modelling
correctly, which is an ongoing research task.
You could look at these some of the following articles by our
cosmology group for more details of this class of explanations for
dark energy and for the Hubble constant puzzle, although this work is
still research in progress:
* https://ui.adsabs.harvard.edu/abs/2013JCAP...10..043R
* https://ui.adsabs.harvard.edu/abs/2013IJMPD..2241018R
* https://ui.adsabs.harvard.edu/abs/2015CQGra..32u5021B
* https://ui.adsabs.harvard.edu/abs/2016IJMPD..2530007B
Cheers
Boud

Bonjour Mathieu,
(1) L'image à l'URL suivant montre, sur une carte tout-ciel
(projection azimutale équivalente de Lambert), la meilleure solution
en position céleste des six axes du modèle dodecaèdral selon les
données de WMAP :
http://cosmo.torun.pl/foswiki/pub/Cosmo/CosmoProjects/RBSG08_CCBYSA_GPL_GFD…
Tel qu'indiqué dans son nom, l'image est republiable sous une licence
au choix - GPL, GFDL ou CC-BY-SA [1]. Elle est refaite indépendamment des
figures de nos articles scientifiques, afin d'éviter des ennuis de
complications des droits d'auteur. Elle est correspond à la Fig. 5a de
RBSG08 (Astronomy & Astrophysics 486 (2008) 55,
http://arxiv.org/abs/0801.0006), où nous utilisions une nouvelle
méthode - celle des corrélations croisées.
Dans un sens, l'image est une prédiction de ce que l'on attend d'une
analyse semblable des cartes de Planck, car c'est ce qui sort des
données de WMAP. Si c'est le bon modèle, Planck devrait le confirmer.
(2) La signification statistique de notre deuxième analyse avec la
méthode des corrélations croisées (RBG08, Astronomy & Astrophysics 492
(2008) 673, http://arxiv.org/abs/0807.4260) est indiquée dans
l'abstract :
"We infer that for an infinite, flat, cosmic concordance model with
Gaussian random fluctuations, the chance of finding _both_ (a) a
large scale auto-correlation as weak as that observed, _and_ (b) a
PDS-like signal similar to that observed is less than about 0.015%
to 1.25%."
(3) Le rôle le plus important de Planck serait probablement de donner plus
de confiance dans l'analyse et dans la soustraction de l'avant-plan
galactique surtout sur les grandes échelles, et de confirmer - ou
réfuter - le manque de structures aux échelles au-dessus de
10 Gpc/h (voir les analyses de Copi et al 2007, 2009, 2011, citées dans
RK11: Astronomy & Astrophysics 533 (2011) A11,
http://arXiv.org/abs/1106.0727) ou la Fig. 1 de RBG08. Le manque de
structures sur les plus grandes échelles a été prédit par Starobinsky
et Stevens et al en 1993 (références dans RBSG08) et c'est ce qui
est observé - si nous acceptons les données CMB de WMAP.
Il y a nombreuses incertitudes qui compliquent l'analyse des
données du fond diffus pour l'analyse de la forme de l'Univers.
D'après notre analyse la plus récente (RK11), les toutes premières
galaxies les plus rares devraient être topologiquement lentillées -
dans certaines positions - aux redshifts de z = 106 \pm 18 environ.
L'existence (avec étoiles allumées) de telles galaxies rares est
actuellement à la limite théorique, et leur détection observationnelle
dans les ondes sous-millimétriques est bien hypothétique.
Pourtant, le lentillement topologique des objets effondrés
gravitationnellement serait moins assujetti au doute que l'analyse
du fond diffus.
Bien cordialement
Boud Roukema
[1] http://creativecommons.org/licenses/by-sa/3.0/

hi everyone,
i've tried to come up with a proposal compatible with the summary here:
http://cosmo.torun.pl/pipermail/cosmo-torun/2006-February/000353.html
and Andrzej's suggestion here:
http://cosmo.torun.pl/pipermail/cosmo-torun/2006-February/000354.html
The proposed text is between ######### - i'm not sure if Bartek or Andrzej
want to sign, or even if this is compatible with Andrzej's arguments,
though i think it should be, because all the material is protected (well,
open) under GFDL copyright, but it's not especially linked to any of our
names - there are typically anywhere between 5 and 100 authors on the wikipedia
page articles.
The LambdaCDM article presently says nothing about "bringing down the
concept of flat and infinite universe" - which IMHO is rather
premature anyway - IMHO that wikipedia page would be a good place to
discuss that - in the wikipedia context - *if* anyone really wants to
have a "public, pedagogical" debate.
Kristen Eisenberg
Billige Flüge
Marketing GmbH
Emanuelstr. 3,
10317 Berlin
Deutschland
Telefon: +49 (33)
5310967
Email:
utebachmeier at
gmail.com
Site:
http://flug.airego.de
- Billige Flüge vergleichen

witam Wiedza i Życie,
Marek Oramus przygotował wywiad z mną, wynikiem wielu dni wielu godzin
dyskusji mejlowe i na żywo, i jeśli dobrze rozumiem, będzie dziś
Was to wysyłać jako propozycję artykułu. Się cieszę, że
mogłbyście publikować popularno-naukowo artykuł o Wszechświecie, ponieważ
wydaje mi się, że interesowałby Wasz czytelników.
Mam jednakże uwagę dotyczący zaproponowanego tytułu, ,,Wszechświat
jako piłka futbolowa". Jest to problematyczny dla wielu powodów:
* Tytuł powinno ściągniąć uwagi czytelniki, ale nie na kosztu błędów
pedagogicznych, wprowadzających czytelniku do błędnego zrozumienia:
* futbol nie daje żadna intuicja dotycząca brak granic, jednakże
brak granic to pojęcie kludzowe;
* futbol nie daje żadna intuicja dotycząca całości przestrzeni
(prawdy pomysł) zamiast coś wewnątrz przestrzenie (błędny pomysł,
dotyczący modelu Wszechświata), raczej powrotne - wszyscy mają
intuicję futbolu jako obiekt, który dużo się rusze w przestrzeni.
* futbol ma 32 ściany, tzn wiele więcej niż 12-ściana (domen
fundamentalny modelu przestrzeni dwunaśtościanowej Poincarego ma
dokładnie 12 ściany), jest zewnętrznie 2-sferycna wersja 20-ściany z
obciętymi rogami; to prawda, że kilka z ścian futbolu są piątokątami
(te czarnymi), ale gdyby chcielibyśmy zmienić futbol do 12-ściany,
mielibyśmy kroić futbol w takim sposobie, gdzie usuniemy całych te
12 widocznych ścian piątokątymi.
O tym drugim punkcie, jak na pewno dobrze wiedzcie, ponieważ
publikowaliście artykuły popularno-naukowe od dawna, prezentacji
Wszechświat Big-bangowy jako obiekt *wewnątrz* przestrzeń, to
jeden z głównych błęd w popularizacji kosmologii.
Przypominam o kartą etyczną mediów z Stowarzyszenia Dziennikarzy
Polskich z 29 marca 1995r.:
http://pl.wikipedia.org/wiki/Karta_Etyczna_Mediówhttp://www.radaetykimediow.pl/dokumenty_kmp1.html
Zobacz ,,zasada prawda" a także ,,Zasada pierwszeństwa dobra odbiorcy":
,,co znaczy, że podstawowe prawa czytelników, widzów i słuchaczy są
nadrzędne wobec redakcji, dziennikarzy, wydawców, producentów i
nadawców."
Tzn, że prawa czytelników do tytułu, który mówi uczciwie co jest w
temacie artykułu, jest ,,nadrzędne wobec redakcji, dziennikarzy,
wydawców, producentów i nadawców." Ja we wywiadu nigdy polecałem
piłka futbolu jako pomoc dla zrozumienie o co chodzi tematu.
Nie widzę, że precedens łamania praw czytelników w niektórach
czasopismach w USA i UK - tzn twierdząc, że model przestrzeni
dwunastościanowej Poincarego, to podobny do ,,piłka futbolu" - to
dobry argument powtórzyć ten łamania karty etycznej mediów cytowana
wyższej.
Kilka przykładowe pomysły dla tytułu, który mogłby być etycznie
zasadzone:
* ,,Wszechświat skończony bez granic"
* ,,Mały Wszechświat bez granic"
* ,,Wszechświat bez granic"
* ,,Kształt Wszechświata bez granic"
* ,,Wszechświat z prostymi, zamkniętymi pętlami"
ale to tylko przykłady.
Pozdrawiam serdecznie
Boud Roukema
CC: * Marek Demianski, członek Rada Naukowa Wiedza i Życie, i ekspert
naukowy w temacie kształtu Wszechświata;
* cosmo-media, *PUBLICZNIE* archiwizowana, otwarta grupa dyskusyjna
kosmologów toruńskich:
http://adjani.astro.uni.torun.pl/mailman/listinfo/cosmo-media
* Marek Oramus

Bonjour David,
> From dlarousserie(a)sciences-et-avenir.com Tue Jan 20 10:43:18 2009
> Dear Boud Roukema,
>
> I am (always) journalist in France for Sciences et Avenir. I had contacted
> you in 2003 about the shape of the universe.
Oui, oui, je m'en souviens. :)
> I do not know if you are still involved in such topic. But I have to write
Tout à fait.
> (shortly) the story of this research and I need to upgrade my information.
> That's why I hope you could help me (Sorry to write in english because I do
> not remember if you speak french...).
En tant que Français expatrié, il serait dommage si j'oubliais
totalement la langue de Molière...
> Here are my questions.
> How could you summarize the state of the art concerning this topic ?
Les deux premières motivations empiriques pour l'hypothèse de l'espace
de Poincaré - le problème des fluctuations manquantes et la courbure
légèrement positive (Omega_totale = densité totale par rapport à la
densité critique = environ 1.01 ou 1.02 , plus ou moins 0.01 ou 0.02 -
sont devenues plutot renforcées qu'affaiblies. Or, si l'on trouvait
que Omega_totale = 1.002 +- 0.001, l'espace de Poincare serait rejeté
a une très haute signification statistique. Pour l'instant, nous sommes
très loin de là. Aussi, Caillerie et al. (dont JP Luminet) ont fait une
analyse semblable à leur première publiée dans Nature, mais avec beaucoup
plus de précision (plus de modes propres, des harmoniques de l'espace de
Poincaré), soutenant leur premier résultat.
En 2008, le groupe torunien [1] [2] a publié les résultats d'un
nouveau test de l'hypothèse de l'espace dodecaèdral de Poincaré, qui
étend le principe des cercles identifiés.
Un problème pratique du principe des cercles identifiés est que
l'analyse est sensible aux petites erreurs d'angle sur le ciel, aux
contaminations du signal sur les échelles relativement petites, ou
à d'autres effets mal compris sur les « petites » échelles. De plus, le
problème des fluctuations manquantes se voit sur les échelles
angulaires sur le fond diffus au-dessus de 60 degrés. Il est donc
raisonnable de chercher une méthode qui est moins sensible aux petites
échelles.
Le principe des cercles identifiés explique exactement quelles paires
de points sur le ciel devraient être, chacune, une paire de deux
images d'un seul point physique. L'extension de l'idée est de
considérer non seulement deux points sur le ciel correspondant à un
seul point physique, mais plutôt deux points sur le ciel qui
correspondent à deux points proches, sans être (en
général) identiques. Puisque deux points proches sont
(statistiquement) fortement corrélés et deux points lointains sont
(statistiquement) faiblement corrélés, l'on peut chercher des
orientations et tailles du dodecaèdre qui impliquent des ensembles de
paires de points, dont les deux membres de chaque paire sont
apparemment distants entre eux sur le ciel mais sont fortement
corrélés, comme si elles étaient réellement proches, l'une de l'autre.
Cette methode prédit deux choses pour l'hypothèse de l'espace
Poincaré. D'abord, il devrait exister une orientation et une taille
optimales qui donnent des hautes corrélations entre certains points
apparemment éloignées entre eux. Deuxièmement, en comparant les points
sur un côté du ciel avec l'autre, l'espace de Poincaré oblige qu'une
rotation de 36 degrés dans un sens ou l'autre soit appliquée. Or, si
l'on permet que la rotation ait une valeur arbitraire, l'on pourrait
attendre à ce que des corrélations par hasard favorisent un angle de
rotation quelconque, avec peu de chance qu'il soit proche de 36 degrés
ou -36 degres.
L'analyse des données de WMAP montre que les deux prédictions sont
confirmées : la meilleure position en coordonnées astronomiques
impique une relativement forte corrélation entre les points très
éloignés entre eux sur le ciel, et l'angle de rotation favorisé est 39
+- 2.5 degrés. L'hypothèse de l'espace de Poincaré n'a pas seulement
réussi au test, mais elle est devenue plus contrainte, puisque
maintenant nous argumentons que si l'hypothèse est la bonne, les
coordonnées de ses six axes devraient être à quelques degrés près
celles publiées dans nos articles de 2008 [1], [2]. Ces valeurs
changent très peu en analysant les différentes versions de la carte de
WMAP (ILC vs Tegmark et al.; avec ou sans masque pour cacher le plan
de notre Galaxie; données de 3 ans versus données de 5 ans).
Indépendamment, sur le côté théorique, où contrairement au lien entre
la relativité générale et la courbure, il n'existe pas de théorie
liant la topologie de l'Univers à une autre propriété physique, il y a
eu au moins un développement inattendu. Jusqu'ici, nous disions dans
la communauté de la topologie cosmique que la topologie de l'espace
n'avait aucun effet sur les équations d'Einstein. Or, dans un article
théorique du groupe torunien [3], nous avons montré qu'au moins dans
certaines conditions et en utilisant la limite de gravité faible
(newtonienne), la topologie peut bien avoir un effet sur la dynamique.
Résumé grand public très court : Imaginons que tu es proche d'un grand
amas de galaxies à ta « droite » qui t'attire par la force de gravité.
Puisque l'Univers est multi-connexe, il y a deux copies identiques de
cet amas, une lointaine à ta « gauche » et une lointaine à ta « droite ».
Ces deux copies aussi t'attirent vers eux, mais très faiblement.
Les distances à ces deux copies sont presque égales, parce que tu es
proche de la « première » copie de l'amas. Donc, ces deux tirements
faibles dans les deux directions opposées s'annulent - presque.
Pourtant, ils ne s'annulent pas totalement. L'amas « à gauche » est un
peu plus près parce que tu es un petit peu « à gauche » de la
« première » copie. La petite force qui reste après l'annulation des
attractions de ces deux copies distantes te tire, donc, vers la
gauche. Si tu étais encore un peu plus éloigné de la première copie,
cette petite force non-annulée serait un petit peu plus fort.
Ce qui est surprenant est non seulement que cette force résiduelle
existe, mais qu'elle est proportionnelle à ton déplacement par rapport
à l'amas de galaxies. C'est un comportement algébriquement semblable à
celui d'une constant cosmologique !
On ne peut pas pourtant en conclure que la constante cosmologique
soit un effet de la topologie de l'Univers - l'effet aujourd'hui
serait à peu près un milliard de fois trop faible. Mais il reste
très intéressant qu'un lien physique entre la topologie et la gravité
peut exister lorsque nous pensions qu'il n'y en avait pas, au moins
pas de façon si simple.
> When Plank will give data, will you try to test once again special topology
Tout probablement. :)
> or are you working on different topic ?
> Do you think that this data could solve the problem ?
La contrainte la plus intéressante de Planck serait à mon humble avis
celle sur la courbure de l'Univers obtenue en analysant ensemble les
cartes faites par Planck et les mesures des BAO (oscillations
acoustiques baryoniques, voir par exemple [5], lorsque le nom BAO
n'était pas encore utilisé) faites par le télescope SKA (Square Kilometre Array)
et des sondages profonds par exemple par un WFMOS (Wide-Field Multi-Object
Spectrograph) sur le VLT ou Subaru. Si l'on pourrait contraindre le
paramètre de densité totale à, par exemple, Omega_totale = 1.002 +- 0.001,
l'espace de Poincaré serait nettement réfuté, puisque avec les analyses
des groupes Luminet et al. et Aurich et al., et les nôtres, ce paramètre
doit forcément être au-dessus de 1.010 et plutôt serait vers 1.013 à 1.018.
> Are there another alternative exept the Poincare shape ?
Oui, mais les autres espaces de courbure positive valables ont des
propriétés de symmétrie moins belles que celles de l'espace de
Poincaré, et les espaces plats (par exemple, le tore) souffriraient de
l'argument (théorique/intuitif) de fine-tuning. Les jugements
subjectifs du rasoir d'Occam jouent un rôle ici - quels modèles sont
les plus simples ? L'espace de Poincaré est un espace plus simple et
symmétrique que plusieurs autres (dont l'espace euclidéen infini, puisque
l'infini n'est pas du tout simple).
> I think your last publication is compatible with such topology. Does someone
> else confirm these idea ?
> And on the contrary does someone criticize your work ?
J'imagine que tu parles de [1] et [2]. A ma connaissance, pour
l'instant personne autre que Ralf Aurich a essayé notre méthode
étendant le principe des cercles identifiés. Aurich l'a appliqué pour
le cas du tore, plutôt que pour l'espace de Poincaré.
> Could you remember the main motivation of such work please ?
Les motivations principales : (1) tester les prédictions de l'hypothèse de
l'espace dodecaèdral de Poincaré (voir au-dessus); et (2) rendre
l'hypothèse plus concrète en déterminant quelles devraient être ses
coordonnées astronomiques sur le ciel.
Bien amicalement,
boud
PS: Par souci de transparence médiatique, j'envois une copie de ce mél
vers la liste avec archives publiques :
http://cosmo.torun.pl/mailman/listinfo/cosmo-media
Bibliographie:
[1] Roukema et al. http://fr.arxiv.org/abs/0801.0006
2008, Astronomy & Astrophysics 486, 55
[2] Roukema et al. http://fr.arxiv.org/abs/0807.4260
2008, Astronomy & Astrophysics 492, 673
[3] Roukema et al. http://fr.arXiv.org/abs/astro-ph/0602159
2007, Astronomy & Astrophysics 463, 861
[4] Aurich http://arxiv.org/abs/0803.2130
2008, CQG, 25, 225017
[5] Roukema, Mamon, Bajtlik, http://fr.arXiv.org/abs/astro-ph/0106135
2002, Astronomy & Astrophysics 382, 387

Hi Paul,
SERIOUS COMMENTS:
(1) "Six pairs of matched annuli crystalised out of the microwave hiss
- their orientation on the sky corresponding to the 12 faces of a
dodecahedron."
It certainly sounds nice and reads well. :)) However...
The first sentence here is misleading: we searched for the best
orientation of a PDS model, while this sentence suggests that the
dodecahedral configuration was a *result* rather than an *assumption* of
our method. i would suggest something like:
"Their search method for the best orientation on the sky for the 12
faces of a dodecahedron homed in onto one particular,
self-consistent set of directions."
i haven't tried to put any "spice" back into the sentence - that's
your (difficult!) task of trying to do it while retaining scientific
accuracy.
(2) "Roukema's team admit..."
We quite overtly (including in the abstract) state the chance of our
twist angle occurring by chance in a non-PDS model and the method by
which we calculate it. So it's not an admission - it's part of our
research results.
How about "Roukema's team themselves stated/said that..." ?
[The New Scientist also used the word "admit" - that's their
inaccuracy, not ours.]
(3) "a team ... claimed to have found 12 matched circles in the CMB"
This is misleading.
The paragraph i gave you previously was:
http://cosmo.torun.pl/pipermail/cosmo-media/2008-February/000073.html
> In our new paper we use a different (though related) method, which we
> think is more robust than the matched circles method - in some sense
> you could say that it uses thickened matched circles, i.e. annuli,
> even though this is an *interpretation* of the method, not the
> calculation method itself. Since we did find a best solution, and that
> solution has the correct twist angle within the uncertainty estimate,
> and since the cross-correlations for that solution are strong, you
> could loosely say that yes, there really are matched annuli in the
> WMAP data.
This is not the same thing as "claimed to have found 12 matched
circles in the CMB".
If you want to be accurate, i suggest something like:
"a team ... claimed to have found what could be loosely said to be
12 thickened matched circles"
i don't think readers need to have the existence of subtlety hidden
from them - we can avoid giving them the details, but we can't
pretend that something is very simple if it's not so simple.
(4) "team find new evidence that the fundamental shape of the universe
is a dodecahedron"
Wrong. You could put:
"team find new evidence that the fundamental domain of the universe
is a dodecahedron"
or
"team find new evidence that the shape of the universe
is a Poincare dodecahedral space"
or
"team find new evidence that the shape of the universe
is a dodecahedron that wraps around on itself"
(5) Regarding the "map with matched circles"
Since our method was not to search for matched circles, we don't have
a map ready with matched circles shown on it. Of course, what we did
is *related* to matched circles, but the relation is not one-to-one.
What i suggest instead is the "best orientation" all-sky map on this page:
http://cosmo.torun.pl/Cosmo/PressReleaseRBSG08
[ The image was created by me, at home, independently of the corresponding
figure in our Astronomy & Astrophysics article, so you shouldn't
have copyright problems. If formality is needed, then choose one
of the GPL/GFDL/CC-BY-SA licences - probably you would want CC-BY-SA:
http://creativecommons.org/licenses/by-sa/3.0/ ]
If you want to use this, then a replacement for the text:
"team ... claimed to have found 12 matched circles in the CMB - shown here -
corresponding to dodecahedral topology."
could be something like:
"team ... claimed to have found that the best orientation of a
dodecahedron in the sky - shown here - gives the required twist
surprisingly well."
OTHER COMMENTS:
(*) "Torun Centre for Astronomy in Poland"
It would be nice to put the university name as well, in at least one
of the three places:
"Torun Centre for Astronomy of Nicolaus Copernicus University in Poland"
MINOR COMMENTS:
(*) "their theory says the topology of space amounts to"
This is a matter of taste whether to use the popular usage of "theory"
to mean "hypothesis", or rather scientists' use of the word, which
is quite different. Is gravity a theory? Yes, it's a theory. It's a
very well established theory. Try to ignore it and you'll soon end up in
hospital or worse. It's much more than just a hypothesis.
i would put: "their evidence supports the hypothesis that the topology
of space may amount to"
(*) "would look like a cosmic hall of mirrors"
i would put:
"would look something like a cosmic hall of mirrors"
(*) "was pioneered astrophysicists"
missing "by"
cheers
boud

Hi Paul,
On Tue, 19 Feb 2008, Paul Parsons wrote:
> I'm just getting in touch as I'm writing a piece for Focus magazine
[to others on cosmo-media: this is BBC Focus magazine:
http://en.wikipedia.org/wiki/BBC_Focus ]
> about cosmic topology. Jean-Pierre Luminet sent me a press release
> about some work he's involved with on Poincare Dodecahedral
> Structure. In it, he cites a 2008 paper with your good self as lead
i think you mean PDS = Poincare Dodecahedral Space
> author - just wondering if I could run a few quick questions past you
> about this...
Sure.
> What do you think of the idea that we live in a universe with
> dodecahedral structure?
What do i think of the idea that we live in a PDS universe?
My general impression is that the CMB data seem to be successively
pointing more and more towards the PDS model.
Firstly, COBE hinted at a lack of structure on the largest
scales. WMAP, with better resolution, confirmed a lack of structure on
the largest scales (more than 10 Gpc/h), especially when we think in
terms of three-dimensional space rather than just in terms of angles.
The next clue was that WMAP in combination with various other
experiments have continually indicated a positive curvature with the
total density parameter Omega_total somewhere around a few percent
above the density for a perfectly flat universe. Among the positive
curvature models consistent with this estimate, the PDS is probably
the most credible. Thirdly, there have been studies by several groups
using different methods, including our latest work in Torun, which
used a method of analysing the WMAP map which was most likely (if we
assume that the PDS model is wrong) to give evidence *against* the PDS
model, but instead, it gave a valid PDS solution.
So the PDS model does seem to be the more natural interpretation of
the data at the moment. However, we cannot yet say that the infinite
flat model is ruled out to high significance by the data: there are
analyses suggesting that the lack of structure above 10 Gpc/h is just
coincidence, and the Omega_total estimates do not rule out the flat
model to high significance.
> What will the universe look like if our universe really does have
> this dodecahedral topology?
We should find that very high redshift (very distant) objects in some
parts of the sky, seen with our telescopes as they looked a long time
in the past, can be seen in other parts of the sky as they appeared
even earlier, as regions of slightly high density which have not yet
gravitationally collapsed, observed as the "cosmic microwave
background". In other words, we could see a single physical region -
traced by filaments of large scale structure including galaxy clusters
and the most massive galaxies - in two different directions on the sky
as they looked like at two different epochs: firstly at a very early
epoch seen as temperature fluctuations, and secondly at an epoch a
billion years or so later when some of the galaxies and galaxy
clusters have just started to form and give off starlight.
The PDS model is not yet well enough constrained to give precise
coordinates for these matching objects. In our paper
(astro-ph/0801.0006) you'll find our present best estimates together
with some discussion of other groups' work, which give some estimates
of the coordinates needed to calculate this, but from our present
results, these are only approximate.
> I understand that your own work has revealed evidence for this cosmic
> topology in the WMAP data? Tell me more about that.
The full answer is here: http://arXiv.org/abs/0801.0006 e.g. start
from the abstract.
This irc log might help too:
http://cosmo.torun.pl/pipermail/cosmo-media/2008-January/000070.htmlhttp://cosmo.torun.pl/pipermail/cosmo-media/2008-January/000071.html
i assume you want a short, layperson's summary. Let's try the following.
Matched circles are the set of pairs of points at which two
"topologically lensed" copies of a single physical point are seen in
apparent space, on the surface of last scattering, observed as the
cosmic microwave background (CMB), at what seem to be two different space
points, but are really, physically, identical.
We extend this idea by considering pairs of points where two points
distant from one another on the CMB (in the apparent space[1]) are two
points in space which in reality are not exactly identical, but are
just physically *near* to one another (in the fundamental
domain[1]). This allows us to use a larger number of data points in the
maps than for a "pure" circles method, since there are many more pairs of
points which are near to one another rather than exactly at the same
position. We know that points near to each other should be
(statistically) correlated to one another: the temperature
fluctuations should (statistically) be similar to one another at a
pair of close points. So although individual pairs of points with
this new method should not match as well as pairs of points on matched
circles, they should still match fairly well, and there are many more
of them. Also, small errors in choosing the correct orientation and
exact geometry of the dodecahedron should be less important this way.
Using this idea, we searched for the best orientation of a PDS model
which gives high cross-correlations of such would-be nearby pairs in
the WMAP maps. If the PDS model is wrong, then these
cross-correlations should, most of the time, be weak, since the points
in a pair are *observed* in apparent space to be quite far from each
other, in which case the correlations have been measured to be
statistically close to zero.
We also allowed for an arbitrary twist angle to be used when matching
opposite faces of the dodecahedron. This meant that if our search
algorithm (a Markov Chain Monte Carlo method) found any strong signal,
then it would be more likely to find a wrong twist angle than a
correct twist angle for the PDS - unless the PDS model is really
correct.
The result was that both a clear best solution was found, in which
pairs of apparently distant points are in fact strongly correlated to
one another for one particular orientation of the dodecahedral face
centres, and the twist angle for this solution is 39 plus or minus 2.5
degrees, which is surprisingly close to what is required for the PDS
model.
So the PDS had two quantitative predictions for our method: that a
strong correlation should be found for some PDS orientation, and that
the twist angle for this strongest correlation should be close to
either plus or minus 36 degrees. Both were satisfied.
[[1] Since you're writing a general article on cosmic topology, i
presume you'll explain near the beginning what the fundamental domain
and apparent space (covering space) are.]
> PS - one additional question to the ones I sent before... I gather David
> Spergel and Neil Cornish have already tried looking for matching circles in
> the CMB, but found nothing. So how did you and your team manage to get a
> positive result? How does your team's method differ?
> Are there really matched circles in the WMAP data? Will you be able
> to check this to a higher degree of confidence when the Planck data
> are released?
In our new paper we use a different (though related) method, which we
think is more robust than the matched circles method - in some sense
you could say that it uses thickened matched circles, i.e. annuli,
even though this is an *interpretation* of the method, not the
calculation method itself. Since we did find a best solution, and that
solution has the correct twist angle within the uncertainty estimate,
and since the cross-correlations for that solution are strong, you
could loosely say that yes, there really are matched annuli in the
WMAP data.
Whether these annuli can be thinned down into matched circles may not
be as straightforward as it was thought earlier. i think the main
argument comes from the Ulm group (Aurich, Lustig & Steiner): there
are problems trying to go to "high" resolution. We extended from the
circles method to using "nearby" pairs of points and are starting from
the moderately large scale signal rather than the small scale
signals. Other groups have done some work on the very largest scales,
those which have been causing the most controversy since the WMAP data
and analyses first became publicly available.
If the coordinates of our best estimate solution are correct to within
our stated precision, then future work will eventually have to thin
the annuli down to "circles". However, for several different reasons,
this may not be as easy as it might seem.
Planck data will certainly help, but data from many different ground
telescope surveys will probably also be necessary to correct the maps
for various contaminants which are generally thought to be in the
maps.
Our own 32m radio telescope at the Torun Centre for Astronomy is being
used for the OCRA (One Centimetre Receiver Array) project together
with support from Jodrell Bank, for removing foregrounds at very high
resolution: galaxy clusters seen due to the Sunyaev-Zel'dovich
effect. OCRA may contribute by helping to get high resolution coordinates of
the PDS model after (if!) the low resolution model continues to get
more observational support.
> How might we find out the topology of our universe? What experiments
> can we do? Again, will the Planck mission help? Will any other future
> missions help, eg CMBPol?
It's hard to predict which experiment will give a result of high
enough significance to convince the cosmological community (assuming
that the model is indeed correct). It was not easy to predict ahead of
time that the supernovae Type Ia surveys would give the most
convincing evidence in favour of a cosmological constant/dark
energy. Planck will help, ALMA and SKA will help, at very high
resolution, OCRA will help, but most probably it will be a combination
of data from several different space and ground-based telescopes,
along with careful, thorough analyses of the data, making as few
arbitrary assumptions as possible. Possibly one particular experiment
may get the most publicity as "discovering the PDS", but in terms of
real science rather than media attention, my speculation is that it
would most likely be a combination of many different data and
analyses, just like for dark energy.
> To me, the universe wrapping round on itself seems much more natural
> than it being infinite. What do you think?
i agree. i think it is most natural to consider the Universe as a
physical object. After all, the alternative would seem to be... a
spiritual object, in which case we're no longer doing science if we
try to study it. Paraphrasing Janna Levin, most physical objects we
know of have finite masses and sizes; so why should the Universe be an
exception?
> What do you think the next big thing in cosmic topology will be?
Predicting the future in fundamental scientific research, especially
on such a deeply fundamental question, is close to useless IMHO.
Grant committees want that, but i'm not the person who'll give it
to them. If we know the answers ahead of time, then it's not research.
On the other hand, i think most people in the cosmic topology
community would agree that any particular cosmic topology candidate
is, given successively better and better data and analyses, highly
falsifiable: the astronomical coordinates representing the model
imply predictions, which if satisfied should lead to more precise
estimates of the coordinates, which in turn should enable more
precise predictions, creating a tightening cycle of constraints.
If successive steps follow this cycle, then probably most of them
could be considered as "big things".
Hope these answers help... i'd be happy to comment on a draft of the
article before it gets published.
You should see this email on the mailing list archive:
http://cosmo.torun.pl/pipermail/cosmo-media/2008-February/thread.html
cheers
boud

----------------------------------------------------------------------
--- Log opened Mon Jan 21 00:00:04 2008
[...]
13:59 -!- nicolas [...] has joined #cosmo
14:05 -!- You're now known as boud
14:05 -!- mode/#cosmo [+o nicolas] by boud
14:05 <@boud> nicolas salut :)
14:05 <@nicolas> bonjour
14:06 <@nicolas> (non je ne me suis pas trompé j'ai eu peur d'un
quelconque décalage horaire)
14:06 <@boud> :P
14:06 <@nicolas> je t'ai envoyé un mail tout ? l'heure aussi
14:06 <@boud> je vois que bruno est venu a 11:23, sans doute
pour tester, et il a quitte a 11:27
14:07 -!- Bruno [...] has joined #cosmo
14:07 < Bruno> hello there
14:07 <@boud> Bruno hi :)
14:07 <@nicolas> Hello
14:08 < Bruno> Hello Nicolas, . Gaudin, i presume?
14:08 <@nicolas> yes
14:09 < Bruno> well gentlemen, thanks for being willing to be
interviewed
14:09 <@boud> alstublieft
14:09 * boud not sure of the spelling :P
14:09 < Bruno> ?t's perfect, polite version even
14:10 <@boud> :)
14:10 < Bruno> this channel is new to me, do you know if a log
is automatically saved?
14:10 <@boud> i was just going to say that - i am logging
14:10 <@boud> one or both of you can log too, depending on what
client you use
14:11 <@boud> we should decide if we want the log to be private
among us, or should it be considered public
14:12 <@boud> bruno ?
14:12 < Bruno> anything is fine by me, but obviously I will quote
(very little) parts of it in the story, OK
14:12 < Bruno> ?
14:13 <@nicolas> it is boud who decides, I just follow the discuss
..
14:13 <@boud> ok, in that case i propose that after the end of the
discussion, i post a copy somewhere "public" e.g. to the
http://cosmo.torun.pl/mailman/listinfo/cosmo-media mailing list
14:13 < Bruno> ok
14:14 <@boud> if someone accidentally says personal/private type
info, please say so and i'll remove it from the log before posting
14:14 < Bruno> sure
14:14 <@boud> ok, i'm ready for questions...
14:15 < Bruno> well, is the universe finite or not?
14:15 <@boud> i don't know
14:15 <@boud> i would *like* to know that and we have done work
towards answering that question, but that's not the same thing
14:16 < Bruno> what would you argue, after publishing/posting
your last paper?
14:17 <@boud> scientifically, i would say just what is said in
our paper
14:17 <@boud> i guess you want a "popular science" compressed
version...?
14:19 <@boud> maybe something like "the evidence seems to be
cumulating in favour of a finite (PDS) universe"
14:20 < Bruno> well, let me put it this way: the diagrams in
the paper look pretty clear to me
14:20 <@boud> thanks :)
14:20 < Bruno> what would they look like if there was no PDS
signal at all?
14:21 <@boud> to give a fully quantitative answer to that question
would/will require a lot of work
14:22 < Bruno> but would you expect something like a pretty evenly
distributed cloud of dots?
14:22 <@boud> intuitively, yes
14:22 <@boud> probably not totally evenly distributed
14:23 <@boud> but i didn't expect such a strong concentration
14:23 < Bruno> right
14:23 <@boud> however, my intuition does not always much a full,
detailed calculation
14:24 < Bruno> in what essential way does this result differ
from the 2004 result?
14:24 <@boud> probably several ways:
14:25 <@boud> (1) we use a much larger amount of the data (temperature
fluctuations in WMAP map) and should be less sensitive to small
errors
14:26 <@boud> (2) by allowing for arbitrary twist angle, we are
able to use a fairly simple method of estimating the probability
14:26 <@boud> (2 continued) in the 2004 result, we didn't calculate
a formal probability or other statistical statement - in this
case we did
14:27 <@boud> (3) using the new method, the 2004 result is not
a stable solution and leads (through the Markov Chains) to the
new result
14:28 <@boud> ok i think that's the main 3 differences
14:29 <@boud> correction to a line above: "match" not "much"
- however, my intuition does not always match a full, detailed
calculation
14:30 < Bruno> Roger
14:32 < Bruno> could you please explain a bit on (3): has the
PDS orientation moved since then? If so, how?
14:33 <@boud> the coordinates of the face centres of the fundamental
domain of the PDS (the dodecahedron) are listed in the abstracts
of the two articles
14:33 <@boud> l = galactic longitude, b = galactic latitude
14:33 <@boud> they are two very different sets of coordinates
14:34 <@boud> also, in the 2004 article the twist was -36 degrees;
in the new article it is +39 \pm 3 degrees
14:35 <@boud> i'm not totally sure if this is what you mean by
"moved" ?
14:36 < Bruno> well, they didn't really move, probably, but is
there an explanation why the two calculations came out so differently?
14:36 < Bruno> please replace 'probably' with 'of course'
14:36 <@boud> i think that (1) is probably the reason
14:36 < Bruno> right
14:37 < Bruno> what does alpha =~20 mean (if we suppose there
is a PDS universe)?
14:38 <@boud> this is discussed in section 4.2
14:38 <@boud> it means that this method probably does not give
an accurate estimate of alpha - the matched circle size
14:39 <@boud> have a look at Fig 9
14:39 < Bruno> OK
14:39 <@boud> let's suppose that the alpha in the diagram is
the true alpha and that the PDS model is correct
14:40 < Bruno> yes
14:41 <@boud> the matched circle in this diagram consists (in
the plane of the paper or your screen) of just two points
14:41 <@boud> the two points where the two spheres intersect
14:41 < Bruno> hm i understand
14:41 <@boud> ok so far ?
14:41 <@boud> ok
14:41 <@boud> now look at the pair of points P and P'
14:42 <@boud> they are also "fairly" close to one another
14:42 <@boud> they're not exactly at the same point, but they're
close
14:43 <@boud> so, again under the assumption that we have the
correct model here with the correct alpha, the temperature fluctuations
at P and P' should be "nearly" the same - they should be well
correlated
14:43 < Bruno> ok
14:43 < Bruno> is alpha is small
14:43 < Bruno> IF alpha is small, i mean
14:43 <@boud> yes
14:43 <@boud> if alpha is big, the argument is wrong
14:44 < Bruno> ok
14:44 <@boud> now, the whole idea of using the cross-correlation
is that we will include pairs which are "close" such as P and
P', not just points which are "exactly" at the same position
14:45 <@boud> now imagine shifting the left sphere a bit to the
left - keep the right sphere stationary
14:45 < Bruno> ok, i thought you were matching up rings, or is
that the same?
14:46 < Bruno> OK, i shifted the left sphere
14:46 <@boud> "rings" was what i gave the NS reporter at the
last minute when she wanted to write "circles"
14:47 <@boud> i'll get back to "rings" in a moment...
14:47 < Bruno> these reporters...but that's what I understood
from the 1999 scientific american paper by luminet as well,
14:47 <@boud> now that you have shifted the left sphere further
to the left, alpha is smaller
14:47 < Bruno> OK
14:47 < Bruno> yes..
14:48 <@boud> and P and P' are still close - in fact, they are
even closer to one another than before
14:48 < Bruno> uhuh
14:48 <@boud> since our method uses all pairs of points which
are "close", we will find a good correlation for this new, smaller
alpha, even though it's smaller than the true alpha
14:49 < Bruno> I see
14:50 <@boud> so if the true alpha is, say, 40 degrees, then
we should find high cross-correlations not only for alpha = 40
deg, but also for many smaller values of alpha
14:50 <@boud> and also for alpha values a little (but not too
much) bigger
14:51 <@boud> in the figure caption we write this as "approximately
matched annuli" or "approximately matched discs" - if the true
alpha is small enough, then it the full discs (including points
P and P') will be matched
14:51 <@boud> and that gets us to "rings" - "ring" is what i
suggested to the NS reporter as a less frightening (to the lay
public) word than "annuli"
14:52 <@boud> and in fact the latin root of "annulus" is "ring"
(in modern French we have "anneau" for english "ring")
14:53 <@boud> we haven't made a proper model of this, so that
why we say our estimate of alpha should be considered "~" as in
"with a big uncertainty"
14:54 < Bruno> allright, so but to make sure I understand, does
the MCMC look for matched rings/annuli or disks then? (sorry to
be dim, if I am)
14:55 <@boud> (you're not dim - it's the fault of the NS
reporter/method-of-journalism...)
14:56 <@boud> the MCMC is certainly *not* defined to look for
matched annuli/disks
14:57 <@boud> however, to *some* extent what it really does is
probably partly equivalent to looking for matched annuli/disks
14:58 <@boud> it looks for high correlations based on the set
of all points which are "close" under a PDS assumption at a given
orientation, circle size and twist
14:59 <@boud> "close" can be in any direction, but of course
it's related to the PDS geometry/topology
15:01 < Bruno> close in the sense you just explained, right?
15:01 <@boud> yes
15:02 <@boud> figs 2 and 3 show this
15:03 < Bruno> OK, i'm getting there
15:04 <@boud> i think the idea of "matched annuli/disks" is a
useful idea, but there would be several complications to relate
it to what we did - it could probably be the subject of a whole
new article...
15:06 < Bruno> allright, so i'll probably stick with something
more abstract But the idea that two intersecting spheres would
yield a matching ring, even in the PDS model is OK?
15:06 <@nicolas> so boud, the corellation fonction, evaluating
between two "distance" does that all points are in an annuli,
no ?
15:06 <@nicolas> (I am not sure for my english, sorry)
15:09 <@boud> nicolas : i'm not totally sure - maybe, maybe not...
15:10 <@boud> bruno: i agree that two intersecting spheres for
the PDS model should yield "approximately" matching rings, but
there is a complication here:
15:10 <@boud> start with two spheres - these define a pair of
matching circles
15:11 < Bruno> yes..
15:11 <@boud> now we allow these circles to thicken - so they
become annuli
15:11 <@boud> however...
15:12 <@boud> what we see in Fig 9 is that they thicken slowly
outwards, but faster inwards, as we increase from "zero separation"
to "small separation = 'close'"
15:13 <@boud> if we imagine painting some lines along the matched
circles (like in the middle of a road), and then we look at the
"nearly" matching annuli, we will see that the "middle of the
road marker" is not in the middle of the annulus, it's closer
to the outside limit of the annulus
15:14 < Bruno> ok
15:18 < Bruno> ok, it's intricate,I understand. Now a perfect
match in the CMB would mean that the SLS at t=380.000 years doesn't
fit in the universe dodecahedron (assuming PDS), so it 'crosses
itself', yes?
15:21 <@boud> i think that's close enough to correct, except
that better than "universe dodecahedron" would be "fundamental
domain" or "one copy of the fundamental spherical dodecahedron",
though i realise that that might confuse your non-specialist readers...
15:21 <@boud> here, "spherical" means "inside of a 3-space with
positive curvature"
15:21 <@boud> it doesn't mean "like a 2-sphere"
15:22 < Bruno> yes sir, i have to cut corners somewhere, not
only for myself
15:22 <@boud> you could probably say "fundamental dodecahedron"
15:22 < Bruno> I will
15:23 < Bruno> Another thing, I know it's early days, but any
word from A&A? And responses from other colleagues?
15:23 <@boud> we're waiting for a referee report
15:24 <@boud> other colleagues have said they're interested and
are reading our paper...
15:24 <@boud> the time scale for this is months, not days
15:25 < Bruno> i know
15:25 <@boud> (it takes time to properly analyse stuff, check
calculations, recheck, etc. etc. and then write it up consistently
with what you've really done...)
15:26 < Bruno> now is it a problem that you have phi=39 plm 2
instead of 36?
15:27 <@boud> not at all
15:27 <@boud> one sigma difference is reasonable - that's what
uncertainty estimates are all about
15:27 < Bruno> OK
15:28 <@boud> if it turns into 39 pm 0.01 , then of course it
would be a problem for the model
15:28 < Bruno> Right, that would really be something exotic.
Now what's next? wait for Planck?
15:30 <@boud> well, we do have some ideas of other things we
could check, but they're not published yet, and will require a
bit of work...
15:30 <@boud> and of course, Planck will come up with some very
useful new data
15:30 <@boud> getting back to your question about what colleagues
think...
15:31 <@boud> there's a bit of discussion on cosmocoffee about
a totally unrelated paper about results from the ACBAR CMB experiment:
http://cosmocoffee.info/viewtopic.php?t=1038
15:31 <@boud> they don't actually mention what is one of the
more interesting results from the new ACBAR paper
15:32 <@boud> you'll find it on page 14 at the end of section
8.2 of the paper: http://cosmocoffee.info/arxivref.php?file=pdf/0801.1491
15:34 <@boud> they continue to agree with previous results that
the best estimate for the curvature of the Universe is a small
positive curvature: they get Omega_total = 1.03 (errors: +0.06,
-0.04)
15:35 <@boud> this is consistent with a flat universe, but it
also seems that now for several years, people doing this sort
of work continually get Omega_total in the range 1.015 to 1.02
to 1.03
15:36 < Bruno> which is consistent with PDS..
15:36 <@boud> yes - on page 19 we discuss this
15:36 <@boud> section 5.7
15:37 <@boud> especially if the true alpha is about 40-50 degrees
- which gives about 1.015 to 1.018 for Omega_total
15:38 <@boud> as we discussed earlier, in our own work we don't
have a good constraint on alpha, but an alpha value somewhere
near the maximum alpha values in Fig. 8 would be reasonable
15:38 <@boud> would be a reasonable interpretation
15:40 < Bruno> Also 40-50 degrees. Do you suppose we'll know
for (reasonably) sure after Planck? Some other time limit?
15:42 < Bruno> would 40-50 degrees say anything about the size
of the fundamental dodecahedron?
15:42 <@boud> i'll answer the last question first: yes most definitely
15:43 <@boud> alpha is the angular radius of the matched circles
15:43 <@boud> equation (15) gives you the exact formula you need
15:44 <@boud> rSLS is close to 9.5h^{-1} Gpc (where you can
put in h = 0.71 = H_0 / 100km/s/Mpc is the Hubble constant)
15:45 <@boud> it only changes slowly if we change Omega_total
and/or Omega_matter
15:45 < Bruno> but would be the size at t=380 000 years, right?
15:46 <@boud> yes
15:46 <@boud> well, i'm not sure if it's exactly 380 000 years,
i don't usually use a number there...
15:47 < Bruno> Ok,but it has expanded a lot since then, hasn't
it?
15:47 <@boud> each local region has locally expanded by a factor
of about 1100, yes
15:48 <@boud> however, all of this work is done in comoving coordinates
15:48 <@boud> this is a choice of coordinates in which the universe
is static
15:48 <@boud> all the expansion is then put into a variable we
call "the scale factor" - usually written a(t)
15:49 <@nicolas> and comoving coordinates = real coordinates
only actually
15:50 <@boud> from equation (15), since you have rSLS and alpha,
you can deduce R_C
15:50 < Bruno> am I terribly wrong in saying that the fundamental
dodecahedron has grown 1100-fold (if it exists)?
15:52 <@boud> you're correct in saying that, but the same thing
applies to the SLS, it too has grown something like 1100-fold
since when the Universe was ~ 4 x 10^5 years old
15:52 < Bruno> OK
15:53 < Bruno> Well, I think I have probed as far as is possible/useful/bearable
for you
15:53 <@boud> nicolas - i would be careful with the word "real"
here - from a point of view of local physical experiments, comoving
coordinates are just a theoretical construct, and "physical/local/proper"
coordinates are more "real"
15:54 <@boud> well, i was just going to finish with eq. 15...
15:54 <@boud> to talk about a "size" of the fundamental dodecahedron,
there are a few different ways you can define "size"
15:55 <@boud> but one way is to take the distance from one face
centre to the opposite face centre
15:55 < Bruno> yes..
15:55 <@boud> if we are thinking in R^4, then this is an angle
of pi/5 (36 degrees)
15:56 <@boud> so then this "size" is pi/5 * R_C
15:56 <@boud> so then you have it in some length units (e.g.
Gpc)
15:58 < Bruno> and it is...
15:59 <@boud> if i've done it right just now in octave, then
for alpha = 40-50 degrees i get 13-15 h^{-1} Gpc
16:00 <@boud> if you want you can put h=0.71 in that, as some
people do nowadays, but i prefer the old style of using h^{-1}Gpc
as the "length unit"
16:01 <@boud> the diameter of the SLS is around 19 h^{-1} Gpc
16:01 < Bruno> You mean 19 Gpc?
16:01 <@boud> no, i mean 19 h^{-1} Gpc
16:02 <@boud> h = H_0 / 100km/s/Mpc is the Hubble constant
16:02 < Bruno> OK, I understand
16:02 <@boud> for most of the XX century, there was a very big
uncertainty in the value of h
16:03 <@boud> and it cancels out of many calculations
16:03 <@boud> so in many cases, we don't actually need to use
a number there
16:04 <@boud> this is \LaTeX notation h^{-1} = 1/h
16:04 < Bruno> I get it
16:06 < Bruno> Boud, thanks for your patient explanation, I will
do my best to put (some of) it to good use in the piece
16:06 <@boud> ok, my pleasure :)
16:07 < Bruno> one more (slightly off-topic) thing:
[off-topic thing removed from log]
16:12 < Bruno> OK, boud, I'll be in touch then, Nicolas, goodbye
and good luck to you both in getting to grips with the universe
16:12 <@boud> ok, tot siens
16:13 <@nicolas> goodbye
16:13 < Bruno> tot ziens, oant sjen (Frisian)
16:14 -!- Bruno [...] has quit
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