Will the new WMAP3 data challenge the assumption of a spatially flat universe?

[marcus]

**they say look at the volume of the OBSERVABLE UNIVERSE, this is something that hellfire or others here could swiftly estimate as a certain number of cubic lightyears.

they say that they have learned from the WMAP3 data that THE VOLUME OF THE WHOLE UNIVERSE IS AT LEAST TEN TIMES LARGER THAN THE VOLUME OF THE OBSERVABLE UNIVERSE.**

So what? These 'unobservable' universes sound like a 'landscape' to me. But, your point is clear. The gratuitious insult did not go unnoticed.

I'm baffled. No gratuitous insult was intended. What are you talking about?

To repeat, what the authors are attempting to do is to estimate a LOWER BOUND on the size of the universe.

Does anybody else think there is some problem with their lower bound?
Ought they have used other data, such as SDSS?

 

[marcus]

http://arxiv.org/abs/astro-ph/0608017
Revised WMAP constraints on neutrino masses and other extensions of the minimal $\Lambda$CDM model
Jostein R. Kristiansen, Hans Kristian Eriksen, Oystein Elgaroy
7 pages, submitted to Physical Review D

my comment: Still chewing on the WMAP3 data. I like to sample papers every now and then to keep track.
Nothing really remarkable. I will get some exerpts.

===quote===

Data set Observations included
A WMAP
B WMAP + ACBAR + BOOMERanG
C WMAP + ACBAR + BOOMERanG + SDSS + 2dF + SNLS + HST + BBN + BAO
...
...

D. Spatial curvature

Next we add spatial curvature, $\Omega_k$ to our sixparameter model. However, altering the geometry of universe mainly affects the positions of the CMB acoustic peaks, while the likelihood modifications mostly concern the amplitude and tilt of the power spectrum. A priori, one would therefore not expect any significant changes in $\Omega_k$. And as seen in Table V, this is indeed the case. For all data sets, $\Omega_k$ = 0 is within about 1 sigma, in good agreement with the results from the WMAP team [1]. The large improvement of the limits on $\Omega_k$ for data set C can to a large extent be understood by the well-known degeneracy between $\Omega_k$ and h, where negative values of $\Omega_k$ can be accommodated by a small h. I.e., when imposing the HST prior on h, the allowed range of $\Omega_k$ is significantly constrained.

 Data Set      WMAP code      Modified code

A               [itex]-0.057 ^{+0.050}_{-0.056}[/tex]      [itex] -0.057 ^{+0.050}_{-0.057}[/itex]
-               -                                                           -
B               [itex] -0.056 ^{+0.052}_{-0.062}[/itex]       [itex] -0.055 ^{+0.048}_{-0.055}[/itex] 
-               -                                                          -
C         -0.005 +/-0.007               -0.006 +/-0.007

TABLE V: Estimated values for $\Omega_k$.

===endquote====

I've been having trouble getting this transcribed Table V to appear right and be legible. In any case I don't think it matters a lot. But as a sample if you look at case A, the confidence interval for the curvature omega is
[-0.113, -0.007]

that means the confidence interval for total Omega is [1.007, 1.113]
this is close enough to the flat case of Omega exactly equal to 1.000 so that one can say it is consistent with the picture of a spatially flat infinite universe

however as we've noticed before it is also consistent with Omega GREATER than 1, like for example 1.01 would actually be within the confidence interval. And that is consistent with the picture of a positive curved spatially FINITE universe. the term for that is "spatial closure"
the typical picture of a spatial slice would be a 3-sphere------like the familiar balloon 2-sphere except 3D instead of 2D
IT WOULD NOT MEAN A UNIVERSE THAT WILL DO A 'BIG CRUNCH' that kind of "closure" is a separate notion from spactial closure.

a spatial closed universe could expand forever----it is one possible version of the prevailing LambdaCDM model that cosmologists are using.

What I am interested in tracking in this thread is any sign of a shift in what cosmologists tacitly assume to be their typical LambdaCDM case. Do they typically assume spatial infinite (Omega = 1, flat) or do they assume
spatial closure (Omega > 1, "nearly flat" but slightly curved).

 

[marcus]

Another episode in the Omega_total story
http://arxiv.org/abs/astro-ph/0608632
Cosmological Constraints from the SDSS Luminous Red Galaxies
M Tegmark, et al... [umpteen authors]
Comments: SDSS data and ppt figures available at this http URL 36 PRD pages, 25 figs

"We measure the large-scale real-space power spectrum P(k) using luminous red galaxies (LRGs) in the Sloan Digital Sky Survey (SDSS) and use this measurement to sharpen constraints on cosmological parameters from the Wilkinson Microwave Anisotropy Probe (WMAP). ...
... Our results provide a striking confirmation of the predicted large-scale LCDM power spectrum. ...
...
... For LCDM, our power spectrum measurement improves the evidence for spatial flatness, sharpening the curvature constraint Omega=1.05+-0.05 from WMAP alone to Omega_tot=1.003+-0.010. All these constraints are essentially independent of scales k>0.1h/Mpc and associated nonlinear complications, yet agree well with more aggressive analyses where nonlinear modeling is crucial. (Abridged)"

Tegmark et al put it in this interval: [0.994, 1.013]
See their table 3, on page 14

WITHOUT the Sloan Digital Sky Survey, with WMAP ALONE they put it in the interval [1.008, 1.118]
again see table 3

See figures 16 and 17, around page 20. they graphically show how Tegmark et al NARROW DOWN the allowed Omega by supplementing WMAP data with SDSS and stellar ages.

=======always interesting to see how people talk========
Look around page 21

Although it has been argued that closed inflation models require particularly ugly fine-tuning [131], a number of recent papers have considered nearly-flat models either to explain the low CMB quadrupole [132], in string theory landscape-inspired short inflation models, or for anthropic reasons [108, 133, 134], so it is clearly interesting and worthwhile to continue sharpening observational tests of the flatness assumption. In the same spirit, measuring the Hubble parameter h independently of theoretical assumptions about curvature and measurements of galaxy distances at low redshift provides a powerful consistency check on our whole framework. Figures 15, 16 and 17 illustrate the well-known CMB degeneracies between the curvature...and dark energy ...,
the Hubble parameter h, and the age of the universe ...; without further information or priors, one cannot simultaneously demonstrate spatial flatness and accurately measure Omega_Lambda, h or t_now, since the CMB accurately constrains only the single combination... Indeed, the WMAP3 degeneracy banana extends towards even larger Omega_total than these figures indicate; the plotted banana has been artificially truncated by a hardwired lower limit on h in the CosmoMC software...

So the slightly positive curved, spatially closed models are being called NEARLY FLAT. that is the term I need to keep an eye out for.
There is some reason that most researchers have preferred to consider the exactly flat case----the paper suggests some reasons having to do with "ugly fine-tuning the inflation"----and yet some other papers have chosen to consider this case: citations [132, 108, 133, 134]. One of these is a paper [108] which Tegmark wrote himself with Martin Rees.

So I would say, based on a brief inspection, that the paper still favors the flat case but that it has some portions which contemplate the NEARLY FLAT case.

 

[marcus]

http://arxiv.org/abs/astro-ph/0609349
Was the universe open or closed before inflation?
Eduard Masso, Subhendra Mohanty, Gabriel Zsembinszki
5 pages, 3 figures
UAB-FT-609

"If the spatial curvature of the universe at the beginning of inflation is negative, there is an enhancement of the temperature anisotropy of the Cosmic Background Radiation at large angles. On the other hand if at the start of inflation the universe was closed with curvature there will be a suppression of temperature anisotropy at the scale of the present horizon. The observation of a low quadrupole anisotropy by WMAP suggests that the universe was closed with $(\Omega-1)$ of order unity at the time when the perturbation scales of the size of our present horizon were exiting the inflationary horizon."

====exerpt=====
From the analyis of the three year WMAP data [2] it is concluded that a power power spectrum with an exponential cut-off at $k_c/a_0 = 3 \times 10^{-4}Mpc^{-1}$ gives a better chi-square fit for the temperature anisotropy angular spectrum than the nearly scale invariant spectrum predicted by an generic slow roll inflation. If the universe was closed at the time of inflation then there is a natural cut-off of $k^2 = K/a^2_i$.
Running the cmbflat programme of CMBFAST [3] after modifying the primordial power spectrum of scalars by including the extra factor in the square brackets of (43), with $\Omega_0 = 1$
and other parameters as given by the central values of the λ CDM model, [2], we find that a good fit for the low-multipole TT anisotropy is obtained with $|K|/(a_iH_{\lambda})^2 \sim 1$ as shown in Fig.1. Therefore a natural explanation of the low cmb power at low l is that the universe was closed at the start of inflation with $\Omega - 1 \sim O(1)$.

 

[marcus]

More news on this interesting issue---finite or not.

New Wright's new paper
just came out
http://arxiv.org/abs/astro-ph/0701584
discussion section page 14:

"Using all the data together
gives the plot shown in Figure 5. The best fit model is slightly closed with
Omega_tot = 1.011 and M = 0.315. "

Wright is an WMAP princ. investigator.

Here is Wright's paper

Constraints on Dark Energy from Supernovae, Gamma Ray Bursts, Acoustic Oscillations, Nucleosynthesis and Large Scale Structure and the Hubble constant
Edward L. Wright (UCLA)
16 pages, 8 figure

"The luminosity distance vs. redshift law is now measured using supernovae and gamma ray bursts, and the angular size distance is measured at the surface of last scattering by the CMB and at z = 0.35 by baryon acoustic oscillations. In this paper this data is fit to models for the equation of state with w = -1, w = const, and w(z) = w_0+w_a(1-a). The last model is poorly constrained by the distance data, leading to unphysical solutions where the dark energy dominates at early times unless the large scale structure and acoustic scale constraints are modified to allow for early time dark energy effects. A flat LambdaCDM model is consistent with all the data."

the initial announcement of WMAP3 "implications for cosmology" paper by Spergel et al already contained hint of this.
warning: it doesn't prove anything. the INFINITE FLAT universe is still consistent, it just is not the best fit. the best fit is with nearly spatially flat, slight positive spatial curvature and therefore the best fit is spatially finite.

flat would be Omega = 1.00 exactly, the best fit is Omega = 1.011

However as Ned Wright is careful to say: a flat model is "consistent" with the data

 

[marcus]

spatial finite, positive curved gets more thinkable

noose is slowly tightening around the neck of the spatial flat universe assumption

couple of more papers

Bruce Basset et al
http://arxiv.org/abs/astro-ph/0702670
Dynamical Dark Energy or Simply Cosmic Curvature?
Chris Clarkson, Marina Cortes, Bruce A. Bassett
5 pages, 1 figure
"We show that the assumption of a flat universe induces critically large errors in reconstructing the dark energy equation of state at z>~0.9 even if the true cosmic curvature is very small, O(1%) or less. The spuriously reconstructed w(z) shows a range of unusual behaviour, including crossing of the phantom divide and mimicking of standard tracking quintessence models. For 1% curvature and LCDM, the error in w grows rapidly above z~0.9 reaching (50%,100%) by redshifts of (2.5,2.9) respectively, due to the long cosmological lever arm. Interestingly, the w(z) reconstructed from distance data and Hubble rate measurements have opposite trends due to the asymmetric influence of the curved geodesics. These results show that including curvature as a free parameter is imperative in any future analyses attempting to pin down the dynamics of dark energy, especially at moderate or high redshifts."Joanna Dunkley et al
http://arxiv.org/abs/astro-ph/0507473
Measuring the geometry of the Universe in the presence of isocurvature modes
J. Dunkley, M. Bucher, P. G. Ferreira, K. Moodley, C. Skordis
4 pages, 5 figs.
Phys.Rev.Lett. 95 (2005) 261303

"The Cosmic Microwave Background (CMB) anisotropy constrains the geometry of the Universe because the positions of the acoustic peaks of the angular power spectrum depend strongly on the curvature of underlying three-dimensional space. In this Letter we exploit current observations to determine the spatial geometry of the Universe in the presence of isocurvature modes. Previous analyses have always assumed that the cosmological perturbations were initially adiabatic. A priori one might expect that allowing additional isocurvature modes would substantially degrade the constraints on the curvature of the Universe. We find, however, that if one considers additional data sets, the geometry remains well constrained. When the most general isocurvature perturbation is allowed, the CMB alone can only poorly constrain the geometry to Omega_0=1.6+-0.3. Including large-scale structure (LSS) data one obtains Omega_0=1.07+-0.03, and Omega_0=1.06+-0.02 when supplemented by the Hubble Space Telescope (HST) Key Project determination of H_0 and SNIa data."

The point is not whether you like flat or don't like flat. The point is we don't know and ASSUMING FLAT INTRODUCES ERRORS.. Assuming flat encourages circular reasoning (according to Ned Wright) and makes what you do unreliable. This is how Basset et al argue, and they cite Ned Wright too:
===quote Basset===
However, we will show that ignoring Omega_k induces errors in the reconstructed dark energy equation of state, w(z), that grow very rapidly with redshift and dominate the w(z) error budget at redshifts (z > 0.9) even if Omega_k is very small. The aim of this paper is to argue that future studies of dark energy, and in particular, of observational data, should include Omega_k as a parameter to be fitted alongside the w(z) parameters.

Looking back, this conclusion should not be unexpected. Firstly the case for flatness at the sub-percent level is not yet compelling: a general CDM analysis [13 the Dunkley paper], allowing for general correlated adiabatic and isocurvature perturbations, found that WMAP, together with largescale structure and HST Hubble constant constraints, yields
Omega_k = −0.06 ± 0.02.
We will show that significantly smaller values of Omega_k lead to large effects at redshifts z ~ 0.9 well within reach of the next generation of surveys.

Secondly, Wright (e.g.[14]) has petitioned hard against the circular logic that one can prove the joint statement (Omega_k = 0,w = −1) by simply proving the two conditional statements (Omega_k = 0 given that w = −1) and (w = −1 given that Omega_k = 0). ...

Given that the constraints on Omega_k evaporate precisely when w deviates most strongly from a cosmological constant, it is clearly inconsistent to assume Omega_k = 0 when deriving constraints on dynamical dark energy...
===endquote===