New model for the Shape of the Universe?

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The discussion centers on the changing understanding of the Universe's shape, particularly the Poincare Dodecahedral Space (PDS), in light of updated WMAP data. Initial beliefs supported the PDS due to the density parameter Omega being close to 1.02, but recent data has shifted the curvature range, making the PDS less likely within the 95% confidence interval. The author seeks alternative 3D models to replace the PDS and references a paper on topological lensing that may not be applicable due to its earlier publication date. Additionally, the article by Jean-Pierre Luminet highlights the dependence of the power spectrum on the mass-energy density parameter, indicating that while some values fit the WMAP data, they remain statistically unlikely. The conversation emphasizes the need for updated research to explore new models of the Universe's shape.
BigRedJeffro
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It has been my understanding from various articles I've been reading by Jeff Weeks and others that there was a strong belief that the shape of the Universe was the Poincare Dodecahedral Space (PDS), based upon the WMAP data's missing certain larger frequencies and the given range for the curvature from the 3-year WMAP to be 1.02 +/- 0.02. That range went from 1.00 to 1.04 in the 3 year WMAP data to approximately 0.9934 to 1.0178 in the 5-year WMAP data (using the LAMBDA version). I read that the shape of the Universe being the shape of the PDS rested largely on Omega being close to 1.02, which was well within the previous range for the density/curvature of the universe. Now that the range has altered, it seems that the PDS is not as likely to be the shape of the Universe, at least it is outside of the 95% confidence interval. Has anyone heard of any other proposed 3D models that would replace the PDS?

I'm currently reading through Topological Lensing on Spherical Spaces by Gausmann, Luminet, Weeks and others which is a paper that classifies positively curved 3D spaces. You can find the paper at the link:
http://arxiv.org/PS_cache/gr-qc/pdf/0106/0106033v1.pdf

However the paper was written well before the most recent data from the WMAP was released and I doubt I will be able to use it to determine the new model, so if you can point me in a better direction with a different paper that would be appreciated as well.
 
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The article "The Shape of Space after WMAP data" by Jean-Pierre Luminet states that:

"The associated power spectrum, namely the repartition of fluctuations as a function of their wavelengths corresponding to PDS, strongly depends on the value of the mass-energy density parameter. Luminet et al. (2003) computed the CMB multipoles for L = 2;3;4 and fitted the overall normalization factor to match the WMAP data at L = 4, and then examined their prediction for the quadrupole and the octopole as a function of W0. There is a small interval of values within which the spectral fit is excellent, and in agreement with the value of the total density parameter deduced from WMAP data (1:02§0:02). The best fit is obtained for W0 = 1.016 (Fig. 9)"

This is not outside of the 95% confidence Interval I stated in the original post, however it is more towards the extremity, leaving it statistically unlikely to pan out.
 
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