The Natural Philosophy Of The Cosmos (a)

The atural Philosophy of the Cosmos (A) Riccardo C. Storti1 1 Delta Group Engineering. Abstract The principles of mass-energy distribution and similitude by Zero-Point-Field (ZPF) equilibria are utilised to derive the values of “H0” and “T0”; where, “T0” [2.7248 (K)] is derived from “H0” [67.0843 (km/s/Mpc)]. The values derived arise by assuming that the “Primordial Universe” was analogous to a homogeneous Planck scale particle of maximum permissible energy density, characterised by a single wavefunction. Simultaneously, the “Milky-Way” is represented as a Planck scale object of equivalent total Galactic mass “MG”, acting as a “Galactic Reference Particle” (GRP) characterised by a large number of wavefunctions with respect to the solar distance from the Galactic centre “Ro”. This facilitates a comparative analysis between the Primordial and Galactic particle representations by application of a harmonic relationship, yielding “H0” in terms of “Ro” and “MG”. Consequently, utilising the experimental value of “T0”, improved estimates are derived for “Ro” and “MG” as being “8.1072 (kpc)” and “6.3142 x1011 (solar-masses)” respectively. The construct herein implies that “Accelerated Cosmological Expansion” is attributable to the determination of the ZPF energy density threshold “UZPF” being “< -2.52 x10-13 (Pa)” [i.e. “< -0.252 (mJ/km3)”]. Moreover, it is graphically illustrated that the gradient of the Hubble constant in the time domain is presently positive (i.e. “dH/dt > 0”). Keywords: CMBR, Cosmological Expansion / Inflation, Dark Energy / Matter, Gravitation, Hubble constant. Introduction Electro-Gravi-Magnetics (EGM) [1, 2, 3, 4, 5, 6] derives critical Cosmological information such as the present values of the Hubble constant “H0” and Cosmic-Microwave-Background-Radiation (CMBR) temperature “T0”. The most important concept developed herein is that “Dark Matter / Energy” is not required to mathematically articulate and precisely numerically determine “H0” and “T0”. The “Accelerated Cosmological Expansion” phenomenon (i.e. “dH/dt > 0”) is derived organically from Particle-Physics, in favourable agreement with experimental evidence. Therefore, it is proposed that the observational inference for the existence of “Dark Matter” from flat Galactic rotation curves, may be explained by halos of ejected Gravitons; i.e., populations of conjugate wavefunction pairs of non-zero mass Photons. Moreover, it is demonstrated in [4] that “Dark Energy” is analogous to the Zero-Point-Field (ZPF) energy associated with the Casimir Effect, acting on a Cosmological scale. Materials and Methods Invoking principles of similitude, “H0” is derived by relating the Polarisable Vacuum (PV) spectrum of a “PlanckParticle” to the present-day utilising the “Milky-Way” Galaxy as a basis for comparison. Within the EGM construct, a “Planck-Particle” denotes the condition of maximum permissible energy density, representing the Universe compacted to a point. As mass-energy density increases, the PV modal bandwidth compresses such that for a particle approaching the Planck Scale, the PV spectrum converges to a single mode approaching the Planck Frequency. Galaxies are homogeneously distributed throughout the Universe and are “approximately” in the same stage of evolution. Hence, it follows that we may utilise our own “Milky-Way” Galaxy as a universal reference to yield an average value of Cosmological gravitational intensity. Utilising astronomical estimates of Galactic radius “Ro” and total mass “MG”, we may represent the “Milky-Way” as a particle at the centre of the galaxy, termed the “Galactic Reference Particle” (GRP). The radiant gravitational intensity of the GRP may be calculated from its PV spectral limit. The GRP is representative of the total mass-energy density and vacuum equilibrium state of the Universe at the present time, as viewed by instrumentation within our solar system. Thus, “H0” is derived by comparing the “Planck-Particle Universe” at the instant of creation to the GRP, facilitated by utilisation of the harmonic representation of fundamental particles. Relating the “Cosmological Expansion” of the primordial “Planck-Particle Universe” to the GRP yields an expansive scaling factor “KT”. Subsequently, Wien’s displacement constant is applied to determine a thermodynamic scaling factor “TW”; quantifying the manner in which Photons radiated at the instant of the “Big-

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Bang” have red-shifted to the microwave range after Hubble time. The microwave frequency is converted to temperature by relating “KT” and “TW”, producing a value of “T0” precisely matching physical measurement. Analysis EGM models mass-objects as being in equilibrium with the Quantum Vacuum (QV) such that the energy state of matter describes the energy state of the vacuum. Consequently, the “Cosmological Inflation” and “Accelerated Cosmological Expansion” phenomena emerge naturally within the EGM construct and are not presumed “a priori” as part of the modelling process. The EGM construct generates the “Cosmological Inflationary Epoch” from first principles, derived from Particle-Physics. The resulting history of the CMBR temperature corroborates with all epochs of “Cosmological Evolution” as predicted by the Standard Model of Cosmology (SMoC). The theory of early “Cosmological Inflation” is reinforced and “Accelerated Cosmological Expansion” is derived. Even though the “Cosmological Inflation Epoch” is a contrivance introduced to fit the “Big-Bang” theory, EGM substantiates its inclusion because it emerges as a natural consequence of the derivation of “H0” and “T0”. However, community understanding of “Dark Energy / Matter” must be questioned as the EGM method predicts “H0”, “T0” and “Cosmological Inflation / Accelerated Expansion”, without invoking “Dark Matter or Energy”; producing results substantially more precise than the SMoC. The key mathematical facts derived and subsequently analysed in [4, 5, 6] are as follows, Key Mathematical Fact Dark Matter / Energy required Maximum Cosmological Temperature ≈ 1031 (K) Big Bang Temperature = 0 (K) Unification with Particle-Physics Relationship between “H0” and “T0” Precise determination of distinct Cosmological evolutionary phases Sign of the Deceleration Parameter is in agreement with expectation Prediction of “Accelerated Cosmological Expansion” Table 1: SMoC vs. EGM

SMoC Yes Yes No No No No No No

EGM No Yes Yes Yes Yes Yes Yes Yes

Results and Discussion The EGM construct implies that “Accelerated Cosmological Expansion” is attributable to the determination of the ZPF energy density threshold “UZPF” being “< -2.52 x10-13 (Pa)” [i.e. “< -0.252 (mJ/km3)”]. Moreover, it is graphically illustrated that the gradient of the Hubble constant in the time domain is presently positive (i.e. “dH/dt > 0”). Subsequently, it is mathematically demonstrated that the magnitude of the impact of “Dark Matter / Energy” upon the value of the Hubble constant and CMBR temperature is “< 1 (%)” such that the Universe is composed of: • “> 94.4 (%) Gravitons”, “< 1 (%) Dark (i.e. inexplicable) Matter / Energy” and “4.6 (%) Atoms”. Refer to “Appendix A” for simulation results produced utilising the MathCad computational environment. Conclusions The PV model of gravity represents a useful and complimentary alternative to General Relativity (GR). References [1] Derivation of the photon mass-energy threshold; Riccardo C. Storti and Todd J. Desiato, Proc. SPIE 5866, 207 (2005), DOI:10.1117/12.614634 {available for download as Ch. 3.8 in [5]}. [2] Derivation of the photon and graviton mass-energies and radii; Riccardo C. Storti and Todd J. Desiato, Proc. SPIE 5866, 214 (2005), DOI:10.1117/12.633511 {available for download as Ch. 3.10 in [5]}. [3] The natural philosophy of fundamental particles; Riccardo C. Storti, Proc. SPIE 6664, 66640J (2007), DOI:10.1117/12.725545 {available for download as Ch. 4 in [6]}. [4] Quinta Essentia: A Practical Guide to Space-Time Engineering – Part 4; Riccardo C. Storti, ISBN-13: 9781847533548, LuLu Press {available for download: http://www.lulu.com/content/795547}. [5] Quinta Essentia: A Practical Guide to Space-Time Engineering – Part 3; Riccardo C. Storti, ISBN-13: 9781847539427, LuLu Press {available for download: http://www.lulu.com/content/471178}. [6] Quinta Essentia: A Practical Guide to Space-Time Engineering – Part 2; Riccardo C. Storti, & G. S. Diemer, ISBN-13: 978-1847993618, LuLu Press {available for download: http://www.lulu.com/content/1540406}. 2

Appendix A

Figure A1: Average Cosmological Temperature vs. Hubble Constant {http://www.lulu.com/content/2588584}. Note: The “Mag. of Hubble Constant” (i.e. “|H|” in “Fig. A1” and the graph title of “Fig. A2”) is an abbreviated reference to the square-root of the magnitude of the rate of change of the Hubble Constant in the time domain (required due to text field character limitations). The value of the Hubble Constant at “t1” is graphically stated in “Fig. A1”; “|H| = √|dH/dt| = 0” denotes the instant when “dH/dt = 0” (as represented by the equations in “Fig. A2”).

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Figure A2: (i) Magnitude of the Hubble Constant vs. Cosmological Age, (ii) 1st Derivative of the Hubble Constant in the Time Domain vs. Cosmological Age {http://www.lulu.com/content/2486994}. Note: the graph title is an abbreviated reference to the square-root of the magnitude of the rate of change of the Hubble Constant in the time domain (required due to text field character limitations). The logic for the specified abbreviation arises twofold; (i) from two distinct numerically coincident derivations of “H0” within the EGM construct such that, for the present day, “√|dH/dt| = H0” (see [4] for details) and (ii), to visually accentuate curve characteristics at ‘t4”. 4