If one allows more general 1-D curves as curves of coherence one can perhaps consider something like this.
- These curves should correspond to intersections of 2-D surfaces at which the inhomogenities of mass density causing the temperature fluctuations tend to be concentrated. There would be enhanced coherence along these surfaces if mass density at these surfaces is reasonably constant.
- The intersections of these 2-D surfaces with the sphere from which the radiation comes from for a given red-shift would define 1-D circles of exceptional coherence. Concentric circles of coherence look something too specific.
- More concretely, what comes in mind at the level of experimental facts are the large voids of scale 108 light years having galaxies at their boundaries. If one believes in fractal universe these kind of honeycomb like structures should appear in a hierarchy of discrete length scales..
One can continue even further to the murky depths of TGD.
- Suppose that one believes that the flatness of 3-space is not due to inflation but due to a period of quantum criticality (dark matter energy as phases with gigantic value of Planck constant). Criticality is characterized by long range fluctuations and fractality. Therefore one indeed expects a fractal honeycomb manifesting itself as a hierarchy of coherence circles in WMAP.
- Diving still deeper and taking seriously p-adic length scale hypothesis, zero energy ontology, and causal diamonds, one would end up with the possibility that the fractal honeycomb with preferred size scales of cells coming as half octaves or powers of two or subset of them. This fractal structure would expand in various scales by discrete jumps involving perhaps the increase of gravitational hbar as the size of CD is scaled up by two.
- We are now very deep -near to the bottom- and there is still some oxygen left which we can waste to our last speculations. Could it be that these astro quantum jumps have occurred even at the planetary level: could large hbar quantum version of Expanding Earth Theory make sense;-). Now we have no oxygen anymore. I am sorry. Maybe I should have warned;-).
- Causal diamonds are defined as intersections of future and past directed light-cones and bring very strongly in mind Penrose diagrams. They indeed define causal units and thus serve as their analogs with upper and lower light-like surfaces of CD serving as the analogs of the conformal infinities at which the positive and negative energy parts of zero energy states reside. Negative/positive energy part of zero energy state looks big crunch or big bang depending on which time direction one looks.
- There would be fractal hierarchy of these CDs within CDs - a fractal hierarchy of cosmologies within cosmologies. Note however that the notion of cosmology is somewhat generalized to include also elementary particles at the lower end of hierarchy;-). For electron with ordinary value of Planck constant this sub-cosmology has duration of .1 seconds in Minkowski time, which happens to correspond to the fundamental bio-rhythm.
Addition: I listened a popular science program about inflation yesterday in radio. These programs are very conservative as is science in Finland but of high quality, which cannot be said about many popular science TV programs made with big money at the other side of ocean.
The possible failure of Gaussianity - meaning a complete absence of long range correlations in the spectrum of temperature (mass density) fluctuations - is the hot topic of cosmology nowadays and the data from Planck satellite might resolve the problem within two years. The claim of Penrose and Gurzadyan is that these correlations are visible already in WMAP data. Note that the appearance of bon-Gaussian correlations is different from what one would expect from field theory models on basis of correlation functions since the prediction is correlations on 2-D surfaces. An interesting possibility is that holography allows ot interpret these surfaces as structures assignable to partonic 2-surfaces.
I learned that the presence of these correlations would kill all inflationary models with only single inflaton field. Theoreticians are however skilled and in the worst horror scenario this could lead to a decades of resuscitation attempts by bringing in more and more complexity. Already now there exists huge number of almost working inflationary scenarios.
Also TGD -or at least a big and beautiful part of it- is in a danger zone. The absence of long range correlations would kill the explanation of flatness of three-space as a consequence of quantum criticality - long range correlations in large range of scales are after all the basic prediction of criticality.
Addition: Lubos Motl wrote a second posting about the finding of Penrose and Gurzadyan. Lubos claims that Penrose and Gurzadyan have rediscovered the already known WMAP excess at L=40 partial wave, which indeed represents deviation from the predictions of the inflationary scenario. This additional exceptionally large harmonic would produce the circles but what is the origin of this harmonics? But could it be just what Penrose and Gurzadyan are claiming or something or just single partial wave which is especially strong and what does this mean? Concentric surfaces intersection the z=constant sphere?
Addition: The preprints of Moss et al and Wehus et al claim that the concentric circles of Penrose and Gurzadyan can be reproduced in simulations. Penrose and Gurzadyan have responded the critics and claim that the simulations cannot reproduce the entire series of circles and that there are also other delicate misinterpretations. Personally I remain confused.
I would be happy if someone would list the reasons for believing that exponential expansion is the only explanation for the flatness of 3-space. Is there convincing evidence for exponential expansion? Or is it only flatness which is seen as evidence for the inflation?
Of course, exponential expansion would smooth out the inhomogenities but Lorentz invariance of the space-time sheet representing cosmological evolution could alone explain this since ground states tend to be highly symmetric. There is also a sequence quantum jumps replacing quantum superposition of cosmologies in 4-D sense (making sense in TGD framework where strong form of holography holds true) with a new one in each quantum jump and this evolution could lead to a situation in which the superposition involves only small deformations of Lorentz invariant cosmology. Kind of approach to highly symmetric ground state but in 4-D sense.