# How To Make Your Universe Model Expand

Posted Jun12-08 at 12:24 PM by jal
Updated Dec20-09 at 01:21 AM by jal

In the 1950’s the expanding universe model was rescued by applying the concept of the phase change of water freezing and thereby getting an inflationary phase for the universe.
They have been working on the math for the last 50 years.

Recently, the observations were made that the universe is expanding faster (accelerating) and that there was DARK ENERGY filling the universe.

I pointed out in “TOMORROWS’ BIG BANG” that the amount of dark energy/matter was “coincidently” in the same range as sphere packing.

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A new concept needs to be found to try to see if it can be made to agree with the observations.
Of course, YOUR MODEL, would need to follow/obey the same “rules”.
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Expansion in the 3rd dimension requires that it follows the INVERSE SQUARE LAW.
It also requires that all units be the same size or have a minimum length.

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Since the bounce has a minimum size of 24 units we can start with densest packing of spheres. [1]
(Densest packing is 12 spheres of equal sizes kissing (touching) a 13th sphere in the center; Hex. or cubic packing)
Therefore, hex. packing has a top row of 3 spheres, center row with 6 spheres around a center sphere, and bottom row with 3 spheres.
If the spheres are all 1 unit in diameter, then we can draw a large sphere around the 12 spheres and it will have a diameter of 3 units.
This larger sphere would not include 6 more spheres of one unit. (3 in the top layer and 3 in the bottom layer)

If we project the diameter of those inner 12 spheres to the surface of the larger sphere then they will make circles of densest packing on that surface. This is also known as Tammes' problem. [2, 3]Those 12 circles also represent the diameter of 12 spheres with a diameter of one unit that are situated around that larger sphere.

We can repeat the exercise and make another sphere around those spheres and the diameter of that exterior sphere will be 5 units. The 12 spheres would be 1/5 the diameter of this larger sphere.
The next sphere will have a diameter of 7 units. The 12 spheres would be 1/7 the diameter of this larger sphere.
etc.
Therefore, the radius of the exterior sphere is increasing by one unit every time we make an expansion step.

All models must be able to answer the following question.
Where are the additional units coming from to fill the available spaces of the expanding spheres?

If the increase of the radius/diameter is done slow enough then the additional units, that are needed to fill the expanding sphere, will have time to get into a perfect hex. pattern before the next expansion step. [2]
Each step for the next largest sphere is predetermined by the size of the units if there is to be hex. packing with no voids.

There is no NEW math or physic proposed for this to happen in 3d.

If your model starts with 2d surfaces then you must include another math process to make the 2d surfaces organize in a sphere.[4, 5, 6, 7, 8]

Have fun!
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The following citations should be sufficient for the more advanced seekers.

[1] http://www.maths.unsw.edu.au/school/articles/me100.html
Distributing points on the sphere
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[2] http://www.mi.sanu.ac.yu/vismath/lub/index.html
Spontaneous Patterns in Disk Packings
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[3] http://www.mi.sanu.ac.yu/vismath/pap.htm
Visual Mathematics Papers
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[4] http://www.enginemonitoring.org/illum/illum.html
Optimal illumination of a sphere
placement problems of points on a sphere.
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[5] http://www.buddenbooks.com/jb/pack/sphere/toggles7.pdf
Multiplicity and Symmetry Breaking in (Conjectured) Densest
Packings of Congruent Circles on a Sphere
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[6] http://www.buddenbooks.com/jb/pack/sphere/intro.htm
Packing Equal Circles on a Sphere (spherical codes)
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[7] http://www.buddenbooks.com/jb/pack/circle/snakes.htm
Spiral Packings of Circles in Circles
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[8] http://www.stetson.edu/~efriedma/cirincir/
Circles in Circles
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The serious model makers would need the following links
http://lts2www.epfl.ch/Main/WS2
LTS2 Collection of Subjects : Wavelets on the Sphere
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http://ltspc89.epfl.ch/~vandergh/ind...G.Publications
Professor Pierre Vandergheynst
The Journal of Fourier Analysis and Applications
Wavelets on the Two-Sphere and other Conic Sections
Jean-Pierre Antoine and Pierre Vandergheynst
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