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Multi-layer Cyclic Universe with number of layers N = 12


An attempt to construct a phenomenological cyclic 12-layer model of the universe.


                                                                                                                                             e^0 = + 1


                                                                                                                                             e^ pii=-1


                                                                                                                                      1+2+3+4+…….= -1/12

                                                                                                                                           Srinivasa Ramanujan




The first multilayer cyclical models of the universe were presented by A. D.  Sakharov in articles[1,2].

In authors phenomenology [3,4] some dates were given in favor of models of this type where the

 universe possibly subject of tangential cycle in articles [5,6,7,8,9,10].

 We call such a model

 Numerological Cyclic Universe. (NCC)

 Space is represented by dimensionless numbers, (the vertical axis)

 Time is represented by dimensionless angles( horizontal axis).

 Period of variation    –pi/2 to +pi/2.   Pic1

Time in has an asymmetric nature and with each step time is compressed as we will show below.  




Notice next sequence….


arc tan 1=45deg. arc tan 2=63.43deg, arc tan 3=71.56deg, arc tan 4=75.96deg, arc tan5=78.69drg, arc tan6==80.53deg, arc tan7=81.86deg. arc tan8=82.93, arc tan9=83.65, arc tan10=84.28deg, arc tan11=84.80deg, arc tan12=85.23deg

 Consider how the difference d (delta) between these angles decreases with each step.

  All numbers are degrees

d1 = 63,43-45=18,43


 d2 = 71,56-63,43=8,13


 d3 =75.96-71.56=4.4


d4 = 78.69-75.96=2.73


d5 = 80,53-78,69=1,84


d6 = 81,86-80,53=1,33


d7 = 82,93-81,86=1,07


d8 = 83,65-82,93=0,72


d9 = 84,28-83,65=0,63


d10 = 84,80-84,28=0,52


d11 = 85,23-84,8=0.43



 Contraction of time d decreased from 18.43 to 0.43


 The gap in degrees is compressed by an order of magnitude.


Attention should be paid to   values of 18 degrees both in the case of elementary particles [3] and in the


 transition from the dimension D=№1 to the D=№2.   Number of dimensions is N= 12 [4]


Apparently 18 degrees is the angular unit of time in our epoch?


What does an angular measure mean? What is the meaning of an angle of 18 degrees?


Age of Universe  10^17sec,  or 10^-17sec, time of life elementary particle.


What mean the same 18 degrees? Our epoch is the transfer from D №1 to D №2 and 18 deg is his Sign.


  Other dimensionless quantity is redshift.


 The redshift is an increase in the wavelength, and corresponding decrease in the frequency and


 photon energy, of electromagnetic radiation (such as light)


    Maximum discovered redshift Z=11.1     Z of CMB are neglected. Paying attention to surprisingly often the


 numbers 11- 12 appears in our calculations, which is close to the maximum number Z=11.  As we assumed this is not a coincidence.


 The value of a redshift   Z, corresponding to the fractional change in wavelength (positive for redshifts),




 by the wavelength ratio 1 + z (which is >1 for redshifts).


The correlation between redshifts and distances is required by all such


 models that have a metric expansion of space. One interpretation of this effect is the idea that space itself is


 expanding.  Consensus among astronomers is that the redshifts they observe are due to some combination


 of the three established forms of Doppler-like redshifts. Expansion of space is basic argument of Big Bang




 Alternative to the Big Bang theory is Static  universe   model, the density of matter in the expanding universe


 remains unchanged due to a


 continuous   creation of matter, thus adhering to the perfect cosmological principle, a principle that asserts


 that the observable universe is practically the same at any time and any place.


Let us return to our NSS cosmology and recall the time in its non-symmetric, or asymmetric,  has


  different "density" (the term of the Russian astronomer Nikolay Kozyrev).


Consequently, the speed of light increases when time contracts.  For example, if time contract to one order


 speed of light increases from 3x10^10 cm/c to 3x 10^11cm/c


Does the supporters of the static Universe are right?  They see only abstract Z= 1, Z = 2, Z = 3,… Z= 11 ?


 They actually see the only transitions from one dimension to another.


Again repeating:


The value of the proton mass [4] increases by an order of magnitude and transfer to another dimension.


 Every step is hit for the next dimension. We have multi-layer space with difference 12 dimensions.


 The proton mass increases with every next spatial step. Electron mass increases by e-fold law


Accordingly, the hydrogen atom undergoes all changes and gradually changes its structure, as evidenced by


 the complex structure of the levels of the hydrogen atom, as well as the existence [5] of the “electron future


 brothers”, the muon and the taon, and of course the second and third generation of quarks.


The cycle ends with a Big Bang, when the mass and charge of the proton and the electron become equal.


 Only the neutron survives, which, due to the weak interaction and the appearance of the proton, electron


 and neutrino, gives birth to the next cycle of the Universe.


In conclusion, consider a table with 3 pictures, from left to right


Pic.2 Mass of Electron rising from 1 to 22 000


Pic.3 Time Deg.(delta) increasing from 18 to 1


Pic.4   Mass of Proton linear rising from N=1 to N=12

and reach to 22 000




 consider some amazing numbers given by in the references:


1.Number of fundamental fermions 12. [8]

2.Number of fundamental bosons 12. [8]

3. Number of dimensions of space 12.[4]

4.Maximum redshift Z=11.

5.tan 18 deg =1/3 [3]

6. Fundamental forces 3 : 1.  Ratio 3:1 [9]

7.ln1839=7.5, ln22050=10.00

  10-7.5=2.5   7.5:2.5 =3:1 [4,9]

All given numbers cannot be coincidence.




1. Sakharov A.D. // Letters ZhETF. 1967.Vol. 5, p. 32.

2. Sakharov A.D. // ZhETF. 1979, vol. 76, p. 1172.

3. https://vixra.org/abs/1806.0382

4. https://vixra.org/abs/2107.0118

5. https://vixra.org/abs/2107.0108

6. https://vixra.org/abs/2107.0126

7. https://vixra.org/abs/2107.0142

8. https://vixra.org/abs/2111.0003

9. https://vixra.org/abs/0907.0008