Die Grundschwingungen des Universums – The Cosmic Unification

Abstract

General relativity theory describes the macrocosm, quantum physics the microcosm. Both fields coact in a natural manner in the universe: Limitations of observation by Heisenberg‘s uncertainty relation and by the Schwarzschild radius cause smallest observable regions. These interact by gravity, perform harmonic oscillations thereby and form the local structure of space. This explains cosmic inflation and solves the flatness problem, the horizon problem, the reheating problem as well as the problem of the big bang singularity. The formation of dark matter is explained additionally.
In the early universe, long-wave fundamental oscillations became effective within the global horizon. These oscillations form the global structure of space as well as the dark energy or vacuum density. This solves the fine - tuning problem. For it the three density parameters, of the vacuum, of radiation and of the dark matter, are calculated directly from the universal constants G, c and h. Moreover the polychromatic nature of the vacuum is realized, the spectrum of the dark energy is calculated and the problem of the significantly different results of the measurement of the Hubble – constant is solved. Thereby the origin of the energy is derived from the universal constants G, c und h.
The theory survives two tests: it fulfills the classical limits and it is in precise accordance with observations. The latter are obtained from the cosmic microwave background and from the observation of distant galaxies.
Links to other fields of knowledge enable an effective understanding. Answers to 42 frequently asked questions provide relations to basic concepts. Exercises with solutions facilitate a deepened understanding and promote the self-reliance.

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Die Grundschwingungen des Universums
-
The Cosmic Unification
This is the Digital Edition of the
English Part only.
Complete Edition:
Verlag Dr. K¨
oster, Berlin
www.verlag-koester.de
ISSN: 2629 1525
permanently available since July 2019
With 8 Fundamental Solutions Based on G,cand h
With Answers to 42 Frequently Asked Questions
Book Series: Universe: Unified from Microcosm to Macrocosm, Volume 1
Hans-Otto Carmesin
27. M¨
arz 2021

Inhaltsverzeichnis
1 German Part 19
2 Cosmic Unification 21
2.1 Introduction ........................... 21
2.2 Observations ........................... 23
2.2.1 Critical density ..................... 23
2.2.2 Density parameters ................... 25
2.2.3 Observation that provides Ωr............. 26
2.3 Purpose of this investigation .................. 27
2.3.1 Age of the universe and time line ........... 28
2.3.2 Numerical input ..................... 29
2.3.3 Parameters to be derived ................ 29
2.4 Usual homogeneous and isotropic model ........... 30
2.4.1 Solution of the FLE ................... 31
2.4.1.1 Integration by parts ............. 31
2.4.1.2 Evolution of densities ............ 32
2.4.1.3 Integral with normalized scale radius . . . . 32
2.4.2 Calculation of the age of the universe ......... 33
2.4.3 Calculation of the light horizon ............ 35
2.4.3.1 Derivation ................... 35
2.4.3.2 Integration .................. 37
2.5 Observable states ........................ 38
2.5.1 Observable structure: definition of IWOSIS ...... 38
2.5.2 Smallest IWOSIS .................... 38
2.5.2.1 Combination of two limitations ....... 38
2.5.2.2 Observation with smallest uncertainty . . . 38
2.5.2.3 Elaboration of the smallest IWOSIS . . . . 40
2.5.3 Smallest ball WOSIS .................. 42
2.5.4 Ball WOSIS due to uncertainty ............ 44
2.6 Newtonian gravity at higher dimension ............ 45
2.6.1 Gaussian gravity .................... 45
2.6.2 Gravitational energy: .................. 46
iii

iv INHALTSVERZEICHNIS
2.6.3 Schwarzschild radius in dimension D:......... 46
2.6.4 Elementary regions ................... 48
2.6.5 Interactions of elementary regions ........... 49
2.6.6 Interactions in the early universe ........... 49
2.6.7 Interaction of two ERs ................. 49
2.7 A model of the universe .................... 50
2.7.1 Basics of the microscopic part of the model ...... 52
2.7.1.1 Isotropy .................... 52
2.7.1.2 Homogeneity ................. 52
2.7.1.3 Modeled ERs ................. 53
2.7.1.4 Fixed density ................. 53
2.7.1.5 General relativity dynamics ......... 54
2.7.2 Quantum dynamics of the microscopic part ...... 55
2.7.2.1 Adiabatic separation of the dynamics . . . . 56
2.7.2.2 Geometric observation of curvature ..... 57
2.7.2.3 Mathematically equivalent dynamics . . . . 58
2.7.2.4 Equivalent physical systems ......... 60
2.7.2.5 Physical equivalence of the two dynamics . 60
2.7.2.6 Dynamics at higher dimension ........ 61
2.7.2.7 Momentum .................. 61
2.7.2.8 Quantization ................. 62
2.7.2.9 Ground state ................. 62
2.8 Solution at high density and small distance .......... 63
2.8.1 Probability density ................... 63
2.8.2 Expectation value of potential energy ......... 63
2.8.3 Convention of potential energy ............ 64
2.8.3.1 Basic idea ................... 64
2.8.3.2 Implementation of the basic idea ...... 65
2.8.4 Enclosed mass ...................... 65
2.8.5 Force generated by enclosed Mor E......... 66
2.8.6 Derivation of expectation value of Epot ........ 66
2.8.7 Limit of high density and short distance ....... 67
2.8.8 Wave function ...................... 68
2.8.9 Fixed point procedure ................. 68
2.9 Approximate solution ...................... 69
2.9.1 Approximations ..................... 69
2.9.1.1 Variational method .............. 69
2.9.1.2 Two cases ................... 70
2.9.1.3 Quantum fluctuations ............ 71
2.9.1.4 Linear approximation ............ 71
2.9.2 Development of the adiabatic separation ....... 71
2.9.2.1 Expectation values .............. 71

INHALTSVERZEICHNIS v
2.9.2.2 Quantum fluctuations ............ 71
2.9.2.3 Implementation of adiabatic separation . . . 72
2.10 Solution for b >> aM...................... 72
2.10.1 Implementation of natural units ............ 73
2.10.2 Approximation of expectation value .......... 73
2.10.3 Classical term ...................... 74
2.10.4 Quantum term ..................... 74
2.10.5 Variation of the fluctuations .............. 75
2.10.6 Dimensional transition ................. 76
2.10.6.1 Procedure ................... 77
2.10.6.2 Critical densities ............... 77
2.10.6.3 Enlargement factor .............. 77
2.10.6.4 Maximal dimension .............. 79
2.10.6.5 Dimensional horizon ............. 80
2.10.6.6 Calculation of the dimensional horizon . . . 80
2.10.7 Dimensional transitions explain inflation ....... 84
2.11 Vacuum part of the model ................... 85
2.11.1 Gravitational waves and ρv............... 86
2.11.1.1 Candidate for the vacuum density ...... 86
2.11.1.2 Basic properties of gravitational waves . . . 87
2.11.1.3 Quantization of gravitational waves ..... 87
2.11.1.4 Zero-point oscillations ............ 88
2.11.2 Densities at Dmax .................... 88
2.11.2.1 Structure of the density ˜ρD,r of radiation . . 89
2.11.2.2 Meaning of the time evolution of the actual
light horizon ................. 89
2.11.2.3 Origin of the density ˜ρD,r of radiation . . . 90
2.11.2.4 Origin of the density ˜ρD,v of the vacuum . . 90
2.11.3 Time evolution of the densities ............ 93
2.11.3.1 Vacuum density during the expansion of space 93
2.11.3.2 ZPO during the expansion of space ..... 93
2.11.3.3 Formed volume during the expansion of space 94
2.11.3.4 Invariant number of ZPOs at a dimensional
transition ................... 94
2.11.3.5 Redshift of ZPO and ZPE at a dimensional
transition ................... 94
2.11.3.6 Modes of ZPO and ZPE at a dimensional
transition ................... 95
2.11.3.7 Time tfof the formation of three dimen-
sional space .................. 95
2.11.3.8 ZPE ˜
Evor ˜
Mvat tf............. 95
2.11.3.9 Density ˜ρvat tf................ 96

vi INHALTSVERZEICHNIS
2.11.3.10 Explicit dependence on Dmax ........ 96
2.11.3.11 Minimum dimension three .......... 97
2.11.3.12 Density ˜ρv,tfand ZPE for Dmax = 301 . . . 97
2.12 Study of the polychromatic vacuum .............. 98
2.12.1 Procedure ........................ 99
2.12.1.1 Procedure at a time tform .......... 99
2.12.1.2 Averaging ................... 99
2.12.1.3 Change ∆Vof the volume .......... 99
2.12.2 Dimensional horizon at tform .............. 101
2.12.2.1 Light horizons ................ 101
2.12.2.2 Dimensional enlargement factor ....... 101
2.12.2.3 Actual light horizon ............. 102
2.12.2.4 Dimensional enlargement factor ZDmax(t0)→D=3 103
2.12.2.5 Light horizon at tf orm ............ 103
2.12.2.6 Evolved light horizon ............. 103
2.12.2.7 Time evolution of the dimensional horizon . 104
2.13 Calculation of the density parameter ΩΛ........... 105
2.13.1 Theoretical input .................... 105
2.13.1.1 Fixed point iteration for density parameter Ωv105
2.13.1.2 Time iteration ................ 106
2.13.1.3 Critical densities ............... 106
2.13.2 Numerical input ..................... 107
2.13.2.1 Input for actual time and matter as reference 107
2.13.2.2 Input for general time and matter ...... 107
2.13.3 Iteration ......................... 108
2.13.3.1 Method of comparison with observation . . 108
2.13.3.2 Λ - CDM model ............... 108
2.13.3.3 Density parameters based on observation . . 109
2.13.3.4 Discrepancy of different measurements of H0109
2.13.3.5 Density parameters based on the present the-
ory ....................... 109
2.13.3.6 Results for each type of evaluation of CMB
data ...................... 110
2.13.3.7 Discussion of the results ........... 110
2.13.3.8 Iteration corresponding to TT,TE,EE + low
E + lensing .................. 112
2.13.4 Solution of discrepancy of Hubble constants . . . . . 114
2.13.4.1 Correction term for H0............ 114
2.13.4.2 Comparison with observations of H0. . . . 119
2.13.4.3 Discussion of modeled values for H0. . . . 120
2.14 Formation of dark matter ................... 122
2.14.1 Local minima as elementary particles? ........ 122

INHALTSVERZEICHNIS vii
2.14.1.1 Exclusion of local minima at D= 3 . . . . . 123
2.14.1.2 Exclusion of local minima at D= 4, D= 5
and D= 6 ................... 123
2.14.1.3 Local minimum at D= 8 .......... 123
2.14.2 Properties of the local minimum at D= 8 ...... 124
2.14.2.1 Inter