Dear Marcelo, everyone,
The topic of Steven Weinberg's rather not-fully-accurate page 9 of his new
book is IMHO rather well-suited to discussing on our public mailing
list rather than privately - this has nothing to do with revealing
unpublished results that we're still working on, it's about correcting
some inaccurate statements regarding cosmic topology.
i also think it would be worth it that the effort we spend in
explaining things to Steven Weinberg can potentially help educate
others directly, i.e. those who may read the mailing list archives or
get pointed there by Big Brother Google Inc. An alternative (and
reasonable) place to discuss this IMHO would be
http://cosmocoffee.info, which is a phpBB based forum for cosmology
research in general, while this mailing list is a mailman mailing
list specifically for cosmic topology.
Anyway, to people who do not have a copy of the book "Cosmology" published
by Steven Weinberg a few days/weeks ago, just email one of us in private
and we can send you a scan of page 9 ("for educational and research purposes
only", to avoid any problems with copyright etc.).
My general opinion:
Yes, i think it would be a good idea to send a message to Steven, and
a consensus message signed by several of us would be a good idea. However,
it would require a bit of work, since ideally it should be:
* clear
* complete
* well-referenced
* but also... reasonably short
This is not so easy, especially keeping it short while satisfying the first
three criteria...
i've posted a suggested draft on our wiki:
http://cosmo.torun.pl/Cosmo/SWeinbergCosmologyPage9Response
and i'm also posting the same initial draft text below here. Personally, i
don't see that there's a huge hurry - i don't imagine OUP issuing a second
edition on a time scale of days or weeks - so i haven't suggested any
time scale. My suggestion is we give people a week or so to update/correct/
complain. If we wait too long, it will soon by the northern summer break
and not much point expecting anyone to respond quickly.
If you want to correct/edit my suggested text and/or sign it, please speak
up! i've tried to be complete in the reference list while limiting to
the precise problems in Steven's text.
cheers
boud
suggested text, openly editable at
http://cosmo.torun.pl/Cosmo/SWeinbergCosmologyPage9Response
----------------------------------------------------------------------
Dear Steven,
We are glad that your cosmology text published by Oxford University
Press a few months ago (March 2008) is, to the best of our knowledge,
the first graduate level type cosmology text in which it is clearly
stated that there are many more than three possible shapes for the
spatial section of our Universe, assuming that the
Friedmann-Lemaitre-Robertson-Walker metric is correct apart from
density perturbations. Nevertheless, some of the statements on page 9
of your book are probably not as accurate as they could be. Here are
some suggestions which should hopefully clarify these issues.
1. "There is no sign of [the same patterns of the distribution of
matter and radiation in opposite directions] in the observed
distribution of galaxies or cosmic microwave background
fluctuations, so any periodicity lengths such as |L_i| must be
larger than about 10^10 light years."
* It is correct that based on cosmic microwave background
constraints (WMAP), it is clear that the in-diameter of
the Universe (see e.g. Fig. 10 of Luminet & Roukema 1999
for various definitions of the comoving size of the
Universe) is greater than 2 h^-1 Gpc.
* However, on a scale of about 12-15 h^-1 Gpc, a large
number of papers have been recently published which
suggest that, in particular, a Poincare dodecahedral space
(for K=+1) or an equi-length 3-torus model (for K=0)
better fit the WMAP data than an infinite K=0 model. There
is not yet any clear consensus on what the data tell us -
some papers argue that the infinite K=0 model cannot be
significantly rejected based on the WMAP data. Please see
the reference list below for the main papers in this
series.
2. "[Most 3-manifolds] ... seem ill-motivated. In imposing
conditions of periodicity we give up the rotation (though not
translation) symmetry that led to the Robertson-Walker metric in
the first place, so there seems little reason to impose these
periodicity conditions while limiting the local spacetime
geometry to that described by the Robertson-Walker metric."
* This is a little unclear. If by "symmetry" you mean the
existence of isometries in the covering space, then there
are no global translation symmetries at all for K=-1 or
K=+1. Translations only exist for K=0. (Clifford
translations exist for some K=+1 spaces, but that's a
separate issue.) If you want to retain translational
isometries in 3-space, then only K=0 is possible, and your
words would seem to describe both K=-1 and K=+1 simply
connected spaces as "ill-motivated".
* More importantly, the Friedmann-Lemaitre-Robertson-Walker
(FLRW) metric only requires local homogeneity and
isotropy, not global homogeneity and isotropy. The FLRW
metric is intrinsically local, it's about the limit of
what happens towards a point. To write this in terms of
practical observational cosmology statistics, consider a
more realistic model of the Universe, i.e. with a
perturbed FLRW metric rather than a perfectly homogeneous
one. In this model, "local homogeneity and isotropy" means
that various n-point auto-correlation functions of
structure tracers within a "neighbourhood" of a Gpc or so
should give identical results to within observational
uncertainties. This is what is observed, but it does not
constrain global homogeneity and isotropy. So it is
unclear why a multiply connected 3-manifold with an FLRW
metric is in any way "limited" or "ill-motivated".
* We are only aware of one paper so far showing that global
topology could have an effect (albeit small) on the FLRW
metric through the addition of an additional acceleration
effect (Roukema et al. 2007).
Best regards,
Boud Roukema, ...
References
o "size of the Universe":
+ Luminet, J.-P., Roukema, B. F., 1999, Topology of
the Universe: Theory and Observation, NATO ASIC
Proc. 541: Theoretical and Observational Cosmology ,
117,
http://cdsads.u-strasbg.fr/abs/1999toc..conf..117L
o WMAP: PDS and 3-torus models (and other spherical models)
vs K=0 infinite model:
+ Aurich, R., Lustig, S., Steiner, F., 2005, CMB
anisotropy of spherical spaces, Classical and Quantum
Gravity, 22, 3443,
http://cdsads.u-strasbg.fr/abs/2005CQGra..22.3443A
+ Aurich, R., Lustig, S., Steiner, F., 2005, CMB
anisotropy of the PoincarĂŠ dodecahedron, Classical and
Quantum Gravity, 22, 2061,
http://cdsads.u-strasbg.fr/abs/2005CQGra..22.2061A
+ Aurich, R., Lustig, S., Steiner, F., 2006, The
circles-in-the-sky signature for three spherical
universes, Monthly Notices of the Royal Astronomical
Society, 369, 240,
http://cdsads.u-strasbg.fr/abs/2006MNRAS.369..240A
+ Caillerie, S., Lachièze-Rey, M., Luminet, J.-P.,
Lehoucq, R., Riazuelo, A., Weeks, J., 2007, A new
analysis of the PoincarĂŠ dodecahedral space model,
Astronomy and Astrophysics, 476, 691,
http://cdsads.u-strasbg.fr/abs/2007A%26A...476..691C
+ Gundermann, J., 2005, Predicting the CMB power
spectrum for binary polyhedral spaces, ArXiv
Astrophysics e-prints, arXiv:astro-ph/0503014,
http://cdsads.u-strasbg.fr/abs/2005astro.ph..3014G
+ Key, J. S., Cornish, N. J., Spergel, D. N.,
Starkman, G. D., 2007, Extending the WMAP bound on the
size of the Universe, Physical Review D, 75, 084034,
http://cdsads.u-strasbg.fr/abs/2007PhRvD..75h4034K
+ Lew, B., Roukema, B., 2008, A test of the PoincarĂŠ
dodecahedral space topology hypothesis with the WMAP
CMB data, Astronomy and Astrophysics, 482, 747,
http://cdsads.u-strasbg.fr/abs/2008A%26A...482..747L
+ Luminet, J.-P., Weeks, J. R., Riazuelo, A., Lehoucq,
R., Uzan, J.-P., 2003, Dodecahedral space topology as
an explanation for weak wide-angle temperature
correlations in the cosmic microwave background,
Nature, 425, 593,
http://cdsads.u-strasbg.fr/abs/2003Natur.425..593L
+ Niarchou, A., Jaffe, A., 2007, Imprints of Spherical
Nontrivial Topologies on the Cosmic Microwave
Background, Physical Review Letters, 99, 081302,
http://cdsads.u-strasbg.fr/abs/2007PhRvL..99h1302N
+ Riazuelo, A., Weeks, J., Uzan, J.-P., Lehoucq, R.,
Luminet, J.-P., 2004, Cosmic microwave background
anisotropies in multiconnected flat spaces, Physical
Review D, 69, 103518,
http://cdsads.u-strasbg.fr/abs/2004PhRvD..69j3518R
+ Roukema, B. F., Bulinski, Z., Szaniewska, A.,
Gaudin, N. E., 2008, The optimal phase of the
generalised Poincare dodecahedral space hypothesis
implied by the spatial cross-correlation function of
the WMAP sky maps, Astronomy and Astrophysics, in
press, arXiv:0801.0006,
http://cdsads.u-strasbg.fr/abs/2008arXiv0801.0006R
+ Roukema, B. F., Lew, B., Cechowska, M., Marecki, A.,
Bajtlik, S., 2004, A hint of PoincarĂŠ dodecahedral
topology in the WMAP first year sky map, Astronomy and
Astrophysics, 423, 821,
http://cdsads.u-strasbg.fr/abs/2004A%26A...423..821R
o effect of global topology on the metric:
+ Roukema, B. F., Bajtlik, S., Biesiada, M.,
Szaniewska, A., Jurkiewicz, H., 2007, A weak
acceleration effect due to residual gravity in a
multiply connected universe, Astronomy and
Astrophysics, 463, 861,
http://cdsads.u-strasbg.fr/abs/2007A%26A...463..861R
----------------------------------------------------------------------
