Chronos said:
I hope you find the other papers interesting. I spent a fair amount of time on that project. The nominal WMAP result [omega = 1.02] predicts a closed universe. I went surfing for some ideas, and that is what I came up with. The last paper in my listing was pretty interesting.
Yes thank you, I did find those papers interesting. However, the need to invoke a multiple connected topology might be stretching the mainstream model a little far to make it fit the WMAP data. Other papers do not find such firm evidence of such topology:
A Hint of Poincar\'e Dodecahedral Topology in the WMAP First Year Sky Map.
Continuing:
SpaceTiger said:
6) The Matter Density
The matter density is, quite simply, the average space density of matter in the universe. It is usually parameterized relative to the critical density:
[tex]\Omega_m=\frac{\rho_m}{\rho_c}[/tex]
This is the density of all non-relativistic matter, including the stuff we're made of (baryonic matter) and the dark matter that has so far eluded our detectors. It does not include photons, relativistic particles, or dark energy.
Since it includes the stuff we can't see, the estimates of [tex]\Omega_m[/tex] must be dynamical; that is, they must be inferred from gravitational influence of the matter. Doing this in a variety of systems (on both small and large scales), we can directly measure the total amount of matter in the universe. These methods tend to give values in the range:
[tex]\Omega_m \sim 0.2 - 0.3[/tex]
Remember that [tex]\Omega_m=1[/tex] would mean that the matter density was exactly sufficient to flatten the universe. Recently, several other independent measurements, including the peculiar velocity field of galaxies, the power spectrum, and the CMB, have given values that are in the same ballpark. In fact, measurements of the matter density have been confirmed in so many different ways that it was previously believed that we lived in an open universe with [tex]\Omega\simeq \Omega_m \simeq 0.3[/tex]. With the recent CMB and supernovae measurements, however, we now believe that the remainder of the energy density required to flatten the universe is in some other form, this mysterious dark energy.
Again thank you to
SpaceTiger for that informative post on the mainstream model.
We note again that, apart from the WMAP data, other measurements of the average density of the universe put
[tex]\Omega_m \sim 0.2 - 0.3[/tex].
The value [tex]\Omega_{total} > 1[/tex] is based on the interpretation of the WMAP anisotropy power spectrum as ‘flat’. That is the distribution of angular diameters of anisotropies of a certain ‘depth’ is as predicted by a spatially flat model. Fitting in other data from the distant SN Ia etc. agrees with a (theory dependent) value slightly larger than 1,~1.02. However, as I have posted above, conformal transformations of the metric leave angles invariant, therefore the data is also consistent with conformally flat models, such as a hyper-cylinder, hyper-cone or torus (locally flat).
The SCC model is highly determined to be either a hyper-cylinder in its Jordan frame or a hyper-cone in its Einstein frame. It is therefore consistent with the WMAP data without the need to invoke "
the remainder of the energy density required to flatten the universe is in some other form, this mysterious dark energy", i.e. it does not need this extra 'epicycle'.
Furthermore, as above it fits the SN Ia data as well.
This highly determined model requires a specific density from first principles, no ‘curve fitting’ or parameter ‘tweaking’ are involved. Just as inflation in its natural form requires a [tex]\Omega_{total} = 1[/tex], so SCC requires:
[tex]\Omega_{total} = \frac 13 = 0.33[/tex]
and a
[tex]\Omega_m = \frac 29 = 0.22[/tex].
The difference:
[tex]\Omega_{fv} = \frac 19 = 0.11[/tex] is required to be that of the false vacuum, i.e. ZPE.
In other words the densities required by the theory are exactly those
as observed and measured by lensing, cluster dynamics and other techniques, moreover, as the false vacuum density is determined to be a finite and reasonable value, it resolves the ‘Lambda’ problem as well.
Garth