The honeycomb of large voids as a tesselation of hyperbolic space by membrane like structures?

Large voids of size scale or order 10⁸ light years forming honeycomb like structures are rather mysterious objects, or rather non-objects. The GRT based proposal is that the formation of gravitational bound states leads to these kinds of structures in general relativity but I do now know how convincing these arguments really are.

One should answer two questions: what are these voids and why do they form these lattice-like structures? Even new physics is allowed!

One explanation of large voids is based on the TGD based view about space-time as a 4-surface in M⁴×CP₂.

1. Space-time surfaces have M⁴ projection, which is 4-D for what I call Einsteinian space-times. At this limit general relativity is expected to be a good approximation for the field theory limit of TGD.

   However, the M⁴ projection can be also 3-D , 2-D or 1-D. In these cases one has what looks like a membrane, string, or point-like particle. All these options are realized.

2. The simplest membranes would look like M¹×S²×S¹, S¹ a geodesic circle of CP₂ which depends on a point of M¹×S² defining M⁴ projection. Only this assumption allows us to have a minimal surface. I discovered this quite recently although the existence of membrane like entities was almost obvious from the beginning (see this).
3. Small perturbations tend to thicken the dimension of M⁴ projection to 4 but the deformed objects are in an excellent approximation still 3-D, 2-D or 1-D.

Membranes are everywhere: large voids, blackhole horizons, Fermi bubbles, cell membranes, soap bubbles, bubbles in water, shock wave fronts, etc.... Large voids could be really voids in a good idealization!! Even 4-D space-time would be absent!! The void would be the true vacuum!

It should be noticed that matter as smaller objects, say cosmic strings thickened to flux tubes, would in turn have galaxies as tangles, which in turn would have stars as tangles. The TGD counterparts of blackholes would be dense flux tube spaghettis filling the entire volume.

What could then give rise to the lattice like structures formed from voids? Here TGD suggests a rather obvious solution.

1. The lattices could correspond to tessellations of the 3-D hyperbolic space H³ for which cosmic time coordinate identified as light-cone proper time is constant. H³ allows an infinite number of tessellations whereas Euclidean 3-space allows a relatively small number of lattices.
2. There is even empirical evidence for these tessellations. Along the same line of sight there are several sources of light and the redshifts are quantized. One speaks of God's fingers. This is what any tessellation of cosmic voids would predict: cosmic redshift would define effective distance. Of course also tessellations in smaller scales can be considered.
3. Also ordinary atomic lattices could involve this kind of tessellations with atomic nuclei at the centers of the unit cells as voids. The space between nucleus and atom would literally be empty, even the 4-D space-time would be absent!
4. Also the TGD inspired model for genetic code involves a particular tessellation of H³ realized at the magnetic body (MB) of a biological system and realizing genetic code. This leads to the conjecture that genetic code is universal and does not characterize only living matter. It would be induced to the space-time surface in the sense that part of tessellation would define a tessellation at the space-time surface. At the level of dark matter at MB, 1-D DNA could also have 2-D and even 3-D analogs, even in ordinary living matter (see this)!

See the article What could 2-D minimal surfaces teach about TGD? or the chapter ZEO, Adelic Physics, and Genes.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.