Mathematical Cosmology

Abstract
- The rate 1.0725 is found frequently between many solar planets orbital and internal distances (a constant rate)
- I suggest this rate is found because of Lorentz Contraction Phenomenon
i.e.
- There's a difference in velocities = "light velocity" between 2 motions in the solar group (even if we can't measure or notice this velocities difference)
i.e.
There's More Than One Frame In The Solar Group

This paper suggests a clear argument as following:
1. The solar group is created by light beams, but we see these light beams in different forms (as matters and distances)

2. We see the light as matter (Specifically, bright fringes produced by light coherence we see as matters, where dark fringes we see as distances)

3. We see bright fringes as matters because our mind works by light velocity (Mind Thinking Process), so the whole matter around us is found because of the human mind effect.

4. to enable us to see the sun rays, Earth has to move with light velocity relative to the sun, to create a difference in velocities = c velocity

5. So, the sun creation depends on the difference in Earth and Sun motions = c velocity.

6. That's why Lorentz contraction phenomenon is seen in the solar orbital and internal distances, specifically with the constant rate = 1.0725, (which equals 7.25%), where the sun obliquity to ecliptic (7.25 degrees).

7. means, the sun creation process contains Lorentz Phenomenon Effect on the solar orbital and internal distances (and on many other values) 
8. The Distance can be defined as "A Form Of Energy", which is proved by the moon orbit regression yearly 19 degrees (Metonic Cycle) (otherwise how distance can move?) (that supports the claim that, distances are dark fringes produced by light coherence)

This Paper Consists Of 2 Parts
1st Part    : Theory Of Matter Creation
2nd Part    : Application on the theory (the solar group creation from the light) 
 Starting From The Solar Group First Energy
 Explaining The Energy Coherence (light coherence)
 Discovering The Matter Creation
 Providing The Solar Group Motions Harmony Reasons

The golden ring to which most physicists aspire is a unified field theory that incorporates all of modern and classical physics. Some scientists and others call this a TOE or ‘theory of everything’, but it is no more than false hubris to believe that humans could possibly know and explain everything about the universe at this time. Einstein chased this goal for the last three decades of his life, basing his theoretical research on his general theory of relativity. Meanwhile, the vast majority of scientists supporting the other major accomplishment of the Second Scientific Revolution were investing all of their time and efforts to advancing the quantum theory and their quest has been extremely successful. They originally had no interest in a unified field theory. After Einstein died in 1955, his efforts were all but abandoned because of his philosophical stance against the prevalent Copenhagen Interpretation of quantum theory even though he had been one of quantum theory’s founders. During the 1970s the tables started to turn and quantum theorists became interested in unifying physics, although not from the foundational principles of relativity theory. They claimed that quantum theory was more fundamental than relativity so they began the same quest from a totally different direction despite their claims to be continuing Einstein’s quest.  Throughout the development of the ensuing standard quantum model, superstring theory and many other theoretical schemes, quantum theorists have remained resolute in their conviction that the quantum and relativity are mutually incompatible so the quantum must completely do away with and replace relativity once and for all. However, the quantum theory and relativity are not actually incompatible and, in fact, say the some of the same things about the nature of physical reality. When the similarities are fully defined and studied and the basic assumptions behind each of the theories are altered to reflect the similarities instead of the incompatibilities, only then can the point of their compatibility be determined and act as a unifying principle resulting in a completed unified field theory of the type that Einstein once sought. The development of this physical model of reality is not without irony. Not only is the quantum theory incomplete as Einstein argued in EPR, but Einstein’s general relativity is also seriously incomplete and true unification cannot be rendered complete at any level of reality until all the theoretical models being unified are themselves complete.

Recent developments within phenomenology have brought to light the indebtedness of phenomenological scientific philosophy to Ancient Greek philosophy. The recent trend that builds on the ancient precedents found in the theories of forms, for example, has demonstrated the importance of the philosophy of Plato and Aristotle for contemporary manifestations of the development of phenomenological eidetic science. This thesis builds on three parallel developments in the phenomenology of time that equally indicate the significance of the ancient Hellenic exact mathematical science of spherical cosmology for the further propagation of phenomenological philosophy. The hypothesis of the infinite sphere gives phenomenology an external foundation capable of accounting for the constitution of the phenomenal universe, possible worlds, and the harmonic continuum of life spanning the inner and outer cosmos. Phenomenological cosmology offers a unified metaphysical framework for first philosophy and the special sciences, with particularly interesting implications for empirical cosmology and theoretical physics. Phenomenology of the spheres brings these phenomenological cosmological insights together in the geometric comprehension of the infinite sphere.

Due to the 20th century mathematical and scientific developments of Georg Cantor, Max Karl Planck, Albert Einstein, and Werner Heisenberg, concepts once relegated to obscurity, such as irrationality, infinity, insolvability, and chaos, were brought to mainstream attention, ultimately changing the course of technological and scientific development into the 21st century. Before these seminal thinkers, concepts like numerical irrationality and infinity were considered by many to be worthless if not amoral; such attitudes can be found persisting back to the ancient Greeks under the Pythagoreans. Interestingly, the aesthetic of irrationality follows a similar historical trajectory, mostly finding relegation in peripheral movements and specific artists before the 20th century. However, the 20th century has seen the greatest and longest persisting resurgence in mathematically irrational thought within the arts. This paper compares the visual and musical experiments in irrationality, incommensurability, and infinity in the works of MC Escher and Conlon Nancarrow during the early and mid-twentieth century, showing a correlation between contemporary mathematical and physical innovations and specific aesthetic pursuits in art and music.

As they tumble through space, objects like spacecraft move in dynamical ways. Understanding and predicting the equations that represent that motion is critical to the safety and efficacy of spacecraft mission development. Kinetics: Modeling the Motions of Spacecraft trains knowledge in rigid body angular momentum and kinetic energy expression shown in a coordinate frame agnostic manner, single and dual rigid body systems tumbling without the forces of external torque, how differential gravity across a rigid body is approximated to the first order to study disturbances in both the attitude and orbital motion, and how these systems change when general momentum exchange devices are introduced.

*Derive from basic angular momentum formulation the rotational equations of motion and predict and determine torque-free motion equilibria and associated stabilities
* Develop equations of motion for a rigid body with multiple spinning components and derive and apply the gravity gradient torque
* Apply the static stability conditions of a dual-spinner configuration and predict changes as momentum exchange devices are introduced
* Derive equations of motion for systems in which various momentum exchange devices are present

We make use of an effective field-theoretical approach to derive post-Newtonian equations of motion of hydrodynamical inhomogeneities in cos-mology. The matter Lagrangian for the perturbed cosmological model includes dark matter, dark energy, and ordinary baryonic matter. The Lagrangian is expanded in an asymptotic Taylor series around a Friedmann-Lemeître-Robertson-Walker background. The small parameter of the decomposition is the magnitude of the metric tensor perturbation. Each term of the expansion series is gauge-invariant and all of them together form a basis for the successive post-Newtonian approximations around the background metric. The approximation scheme is covariant and the asymptotic nature of the Lagrangian decomposition does not require the post-Newtonian perturbations to be small though computationally it works the most effectively when the perturbed metric is close enough to the background metric. Temporal evolution of the background metric is governed by dark matter and dark energy and we associate the large-scale inhomogeneities of matter as those generated by the primordial cos-mological perturbations in these two components with δρ/ρ ≤ 1. The small scale inhomogeneities are generated by the baryonic matter which is considered as a bare perturbation of the background gravitational field, dark matter and energy. Mathematically , the large scale structure inhomogeneities are given by the homogeneous solution of the post-Newtonian equations while the small scale inhomogeneities are described by a particular solution of these equations with the stress-energy tensor of the baryonic matter that admits δρ/ρ 1. We explicitly work out the field equations of the first post-Newtonian approximation in cosmology and derive the

An article by Sabine Hossenfelder and Stacey S. McGaugh, titled “Is Dark Matter Real?’, has just appeared in the August 2018 issue of Scientific American.  Every physicist, astronomer, astrophysicist and cosmologist as well as everyone interested in science needs to read this article because it portends one of the greatest scientific advances in several hundred years, the complete unification of physics and science in general. Due to new observational evidence in astronomy, they have concluded that “Astrophysicists have piled up observations that are difficult to explain with dark matter. It is time to consider that there may be more to gravity than Einstein taught us.” But they have understated the case.

In effect, the new observational data found by McGaugh and an international group of astronomers simply shows that specifically designated dark matter particles do not exist, so the supposed dark matter halos around spiral galaxies do not exist and the rotational speed discrepancies in galaxy orbiting stars and star systems that go unaccounted for by normal gravity are, in fact, due to a secondary effect of normal matter within the galaxy. This finding not only challenges the present theories of gravity (Newtonian and Einsteinian), which it demonstrates are incomplete, it also blows some big logical holes in the fundamentality of the quantum theory, the Standard Model of point-particles and quantum field theories in general that seem to rule the world of modern theoretical physics. Given other recent confirmations of Einstein’s general relativity, found mostly in the detection of gravitational waves that Einstein predicted a century ago, relativity theory seems on the ascendancy and quantum theory is falling behind. The time for a unified field theory that combines the best of both of these paradigms is at hand.

We consider the Universe deep inside the cell of uniformity. At these scales, the Universe is filled with inhomogeneously distributed discrete structures (galaxies, groups and clusters of galaxies), which perturb the background Friedmann model. Here, the mechanical approach (Eingorn & Zhuk, 2012) is the most appropriate to describe the dynamics of the inhomogeneities which is defined, on the one hand, by gravitational potentials of inhomogeneities and, on the other hand, by the cosmological expansion of the Universe. In this paper, we present additional arguments in favor of this approach. First, we estimate the size of the cell of uniformity. With the help of the standard methods of statistical physics and for the galaxies of the type of the Milky Way and Andromeda, we get that it is of the order of 190 Mpc which is rather close to observations. Then, we show that the nonrelativistic approximation (with respect to the peculiar velocities) is valid for $z \lesssim 10$, i.e. approximately for 13 billion years from the present moment. We consider scalar perturbations and, within the $\Lambda$CDM model, justify the main equations. Moreover, we demonstrate that radiation can be naturally incorporated into our scheme. This emphasizes the viability of our approach. This approach gives a possibility to analyze different cosmological models and compare them with the observable Universe. For example, we indicate some problematic aspects of the spatially flat models. Such models require a rather specific distribution of the inhomogeneities to get a finite potential at any points outside gravitating masses. We also criticize the application of the Schwarzschild-de Sitter solution to the description of the motion of test bodies on the cosmological background.

The author's concept  and  postulate  of  what constitutes  the  whole  of  'the  Cosmos'  is:  "All  of  the  Infinite  'Absolute  Space' -'Time' Continuum".

Within this  multi-dimensionally  infinite  'Absolute  Space' -'Time'  Continuum'  there  is containment  of Finite Universes,  which  might  have  some varying  physics  laws  and  likely some  similar physics  laws  and  realities  as were  found  in  our  Universe.  The Universes  can have  varying  shapes,  however if  they  have  a 'cyclical'  existence,  then  their  likely  shapes should  be roughly  spherical,  or  ellipsoidal,  or  related  thereto.  These  Universes,  which  are within the  'Absolute  Space' -'Time' Continuum',  can be continually  evolving  and  their sizes  can  likely  pulsate,  which  means,  expand  and  contract  within  certain  limits.  These limits  can change  from  one  'Universe  Cycle' to  the  next.  The limits  of  expansion  depend on the  degree  of  occurrence of 'photon  decay'  activities,  which  leads  to  'mass'  increase and  on  the  value  of  a 'Maintenance'  Factor,  which  uses  the 'Gravitational  Inflow' mechanism.  This mechanism provides  that  there  is  no energy  loss  of  the  vortex  entities due  to  the  slight  friction,  which  occurs  there  where their  orderly  irrotational  flows  border onto  the  disorderly  'Brownian'  motion of the  cosmic  'Background  Radiation'.  This mechanism  finds  cause  in  the  phenomenon  of  'self-organization'  and  'self-defense' which  is  displayed  by 'closed  vortex  rings'.

'Absolute  Space'  is  everywhere,  also  within the  Universes,  which  are suspended therein.  Within  a  given  Universe, 'Absolute  Space' acts  as  a  'background'  therein,
against  which 'Time'  and  'Coordinates'  in  that  particular  Universe  can be  measured  or compared.

Universes  can  also  be 'super-positioned'  upon  each other, just as  well as  being next  (although  separate)  to  each other. 'Super-positioned'  means  that  one  Universe  is located  within  another  Universe  with the  understanding  that  all  Universes  are  suspended in  'Absolute  Space'.

Why there's No velocity higher than Light Velocity C =300000 km/sec? Because • The Matter is created from light beams coherence (according to Young Experiment-The Main Hypothesis) • The Time is created as the Matter Changing measurement • Our body (matter) is produced by the same method, from this light beams coherence • Our bodies are connected with specific Light velocity and specific time rate because our bodies are produced by specific Light Beams coherence

The life to Earth came from the Universe: the part is alive due to the Entire, this world is alive thanks to the Whole. The first tribe of our Earth w ere Scythians, people from the Moon; their selenic language was the root to earthly languages — the heart of human language. // Жизнь на Землю пришла из Вселенной: часть Целым жива, мир сей — Всем. Племя первое нашей Земли — Скифы, люди с Луны; их язык, корневой земным — лунная молвь, сердце речи людской.

1. The Main Hypothesis: The Matter Is Created From The Light 
2. The produced matter is created in motion, that means the solar planets are created in motions (regardless the motion reason)   
3. The solar group are a group of motions conveyors, So the motions of all solar planets are depended on each other
4. The solar group motions aim to create a difference in motion velocity = C between 2 points in the group.
5. i.e. The Solar Planets work as gears or conveyors group, transfer the motion from point to another point, aiming to create a difference in motion velocity = C velocity. And that's happening where the solar group motions create a difference in velocities between the Earth and Sun motions = C velocity (for that reason the sun is our source of light)
6. The solar group is A Dipole System has 2 heads (the sun and the Earth)
7. The light Production by the planets motions (i.e. by transferring of the mechanical waves into light waves), the original source of light beams energy, from which the solar planets were created, will be conserved. 
8. Because there's a difference in velocity = C between 2 points in the solar group (the sun and the Earth), we may conclude easily that, there's more than one frame in the solar group. 
9. To create a difference of velocity = C, all solar planets should revolve around the dipole line (The Sun-Earth Line) in the same direction, enabling the velocities addition process to gather all motions in the same point…
10. The Produced Solar Planets should have relationships between their Geometrical structures (if they were created from the light), so the planets are not created independent but related to each other geometrically.

The Moon as the only black hole in the Space. // Луна как единственная черная дыра Вселенной.
_____________________

Теории  нашей безбожной науки — намеки на Истину, сокрытую за ними. На Истину, которую сама она не зрит. Такова есть теория дивных уму черных дыр. Человечество, не знакомое ни с одним их реальным образчиком, с тем лишь настырно глаголет о них, что единственная реальная черная дыра Вселенной зияет в шаге от Земли: то — Луна, Мать людей и врата в мир Иной.

Всё сказанное наукой касательно черных дыр относится к ней и ни к чему другому. Но как черная дыра, Луна не такова, как мнят нынче. Вот то, в чем отличие этой дыры НАСТОЯЩЕЙ от ложных, примысленных дыр.

In the framework of a cosmological model of the Universe filled with a nonrelativistic particle soup, we easily reproduce inflation due to the quantum potential. The lightest particles in the soup serve as a driving force of this simple, natural and promising mechanism. It is explicitly demonstrated that the appropriate choice of their mass and fraction leads to reasonable numbers of e-folds. Thus, the direct introduction of the quantum potential into cosmology of the earliest Universe gives ample opportunities of successful reconsideration of the modern inflationary theory.

We calculate the present expansion of our Universe endowed with relict colored objects - quarks and gluons - that survived hadronization either as isolated islands of quark-gluon "nuggets", or spread uniformly in the Universe. In the first scenario, the QNs can play the role of dark matter. In the second scenario, we demonstrate that uniform colored objects can play the role of dark energy providing the late-time accelerating expansion of the Universe.

While the confirmed existence of Dark Matter (DM) and Dark Energy (DE) forms a serious and indeed revolutionary problem for physics, they are actually easy to explain if the reality of a fourth macroscopically extended spatial dimension is assumed. The four dimensionality of space is best portrayed in the case of galactic formation in the early universe, where the DM halo that surrounds spiral galaxies can be modeled. DM is nothing more than spatial curvature in the higher fourth dimension that is not associated with local matter (matter inside the spiral galaxy itself), but is instead the result of an interaction between local matter and the overall curvature of the universe. This model yields a definition of DE that also depends on curvature in the fourth dimension in that it predicts the increasing expansion rate of the universe.
The model is strictly geometrical and it does not readily reduce to a simple algebraic formula. Yet the geometry does lead to testable predictions rendering the model falsifiable and a classical algebraic formula that adequately describes the gravitational source of the DM in the geometry of the fourth dimension does emerge upon further consideration of how galaxies evolve by the accretion of material bodies gravitating toward the central core. This formula can also be quantized and relativized and thus leads to a complete unification of physics that once again establish the fundamental nature of relativity.

Keywords: galactic rotation problem, halo, Dark Matter, CDM, HDM, Dark Energy, General Relativity, Kaluza, Klein, five-dimensional, fourth dimension, space-time, Einstein, positive curvature, extrinsic curvature

In this revisited research thesis, we calculate some Ramanujan expressions concerning the "First letter to Hardy". We describe the possible mathematical connections with some equations and topics concerning the Supersymmetry Breaking, Nilpotent Supergravity and Pre-Inflationary Clues.

v2  -  REVISITED VERSION  -  14.03.2021

In this paper we have described some Ramanujan equations and obtained new possible mathematical connections with ϕ, ζ(2) , Hausdorff dimension values, several equations of Teleparallel Cosmology and Higher-Spin Interactions in String Theory

REVISITED AND DEFINITIVE VERSION  16.12.2020

In this paper we study scalar perturbations of the metric for nonlinear $f(R)$ models. We consider the Universe at the late stage of its evolution and deep inside the cell of uniformity. We investigate the astrophysical approach in the case of Minkowski spacetime background and two cases in the cosmological approach, the large scalaron mass approximation and the quasi-static approximation, getting explicit expressions for scalar perturbations for both these cases. In the most interesting quasi-static approximation, the scalar perturbation functions depend on both the nonlinearity function $f(R)$ and the scale factor $a$. Hence, we can study the dynamical behavior of the inhomogeneities (e.g., galaxies and dwarf galaxies) including into consideration their gravitational attraction and the cosmological expansion, and also taking into account the effects of nonlinearity. Our investigation is valid for functions $f(R)$ which have stable de Sitter points in future with respect to the present time, that is typical for the most popular $f(R)$ models.

This paper is devoted to different modifications of two standard softenings of the gravitational attraction (namely the Plummer and Hernquist softenings), which are commonly used in cosmological simulations based on the particle-particle (PP) method, and their comparison. It is demonstrated that some of the proposed alternatives lead to almost the same accuracy as in the case of the pure Newtonian interaction, even despite the fact that the force resolution is allowed to equal half the minimum interparticle distance. The revealed way of precision improvement gives an opportunity to succeed in solving Gurzadyan's Problem 5 and bring modern computer codes up to a higher standard.

The purpose of this paper is to show how using certain mathematical values and / or constants from a Ramanujan equation, some important parameters of String Theory, Particle Physics and Cosmology are obtained.

UPDATED AND REVISITED VERSION  03.04.2021

The present study, on the expansion of universe, is based on an assumption regarding the possibility of inter-conversion between matter and dark energy, through some interaction of matter with the scalar field in the framework of Brans-Dicke theory. The field equations for a spatially flat space-time have been solved using an empirical dependence of scalar field parameter upon the scale factor. To represent the behaviour regarding the non-conservation of matter, a function, expressed in terms of the Hubble parameter, has been empirically incorporated into the field equations. Their solution shows that, this function, whose value is proportional to the matter content of the universe, decreases monotonically with time. This matter-field interaction generates late time acceleration, causing the deceleration parameter to change its sign from positive to negative. Time dependence of the proportion of dark energy component of the universe has been determined and shown graphically. Time va...

Dark matter makes up about 23% of matter-energy content of the Universe, other components being the normal baryonic matter and dark energy. Apart from the usual structure of dark matter halo around galaxies, simulations of galaxy formation suggests an additional dark matter component in Milky Way mass galaxies similar to the stellar disk of stars in galaxies. Current detection experiment for dark matter are configured for the standard halo structure. In this work we study how the existence of dark matter disk can effect these experiments. More importantly, we focus on the low energy spectrum of WIMP scattering in direct detection experiments and propose lowered threshold in current experiment which can exploit the effects of dark matter disk, if it indeed exists.

In this research thesis, concerning the Srinivasa Ramanujan Manuscripts, we have analyzed various formulas, the Rogers-Ramanujan continued fractions, the mock theta functions and some sectors of Cosmology and Theoretical Physics. We have obtained further new possible mathematical connections and developments

REVISITED AND UPDATED VERSION  18.10.2021

The purpose of this paper is to show how using certain mathematical values and / or constants from a Ramanujan equation, some important parameters of Particle Physics and Cosmology are obtained.


v1  06.02.2020  UPDATED VERSION  14.09.2020

Scalar cosmological perturbations are investigated in the framework of a model with interacting dark energy and dark matter. In addition to these constituents, the inhomogeneous Universe is supposed to be filled with the standard noninteracting constituents corresponding to the conventional $\Lambda$CDM model. The interaction term is chosen in the form of a linear combination of dark sector energy densities with evolving coefficients. The methods of discrete cosmology are applied, and strong theoretical constraints on the parameters of the model are derived. A brief comparison with observational data is performed.

The problem of creation of Unitary Field theory, or the Theory of Everything, which the Einstein was so eager to solve by means of physics, remained unsolved since it is solvable only by means of the Word: because the Word, according to Bible — is the God and «the God has»: Universe, His Child. This particular solution is given by the linguistic work about the Existing, offered by me to you and based on the Pressing method, the founder of which is Dionysus (Bacchus) — the ancient's god of the Word, Moon and Wine. // Познать Мир, Божий Храм - есть познать Слово нам. Слово - это Луна.

In this paper (part III), we analyze several equations concerning Geometric Measure Theory, various Ramanujan parameters and the developments of the MRB Constant. We describe the new possible mathematical connections with some sectors of Cosmology (Bubble universes) and String Theory.

In this research thesis, we have analyzed further Ramanujan formulas and described further new possible mathematical connections with some parameters of Particle Physics, String Theory, Brane Supersymmetry Breaking and Cosmology

v2  -  07.02.2021

In this research thesis, we have described the new possible mathematical connections between some equations of various topics concerning the Bouncing Cosmology, the Cosmological Constraints regarding the Dilaton Inflation and some sectors of Number Theory, principally the Rogers-Ramanujan continued fractions and the Ramanujan's mock theta functions

v1  31.10.2019    UPDATED VERSION  10.10.2020

Below another link of this paper:

http://xoom.virgilio.it/source_filemanager/na/ar/nardelli/michele%20and%20antonio%20papers/Bouncing%20cosmology%20and%20f(T)%20gravity-Number%20Theory%20B.pdf

This summary sheet includes: (1) the “Single Field Theory” (SOFT) equations and their relationships that amount to a final version of Einstein’s unified Field theory; (2) a “Unification Tree” that shows the historical relationship between various unification attempts; (3) the chart “Evolution of Classical Unified Field Theories” that shows the development of Einstein’s and related work; (4) a 1980 diagram of a particle in quantized curved space-time; (5) a more modern depiction of a particle in quantized curved space-time; (6) a rough picture of a Lithium six nucleus that unifies the features of the shell models, fluid drop models, Yukawa potential and quantum tunneling; (6) a graphical representation of the electronic orbits around a nucleus in the context of the quantized space-time continuum; and (7) a graph showing “The Atom as single field potential”.  This Handout from the Vigier IX Symposium accompanied the presentation "Modern Fysics Phallacies: The best way ‘not to unify physics’ turns out to be the only way ‘to unify physics’."

Many physicists believe that the unification of physics within a single paradigmatic theory has been the primary goal in science for only the past few decades, but this would not be true. Unification was the original goal of Einstein and a few other physicists throughout the 1920s to the 1960s during a period of time when quantum theorists were ironing out their own unique set of problems. The unification of physics under the guise of the quantum paradigm only emerged during the 1970s and has since overshadowed all attempts to unify physics from the fundamental principles of relativity. Today too many physicists believe, without any supporting evidence, that the concept of the quantum is far more fundamental than relativity so earlier attempts based on the continuity of relativity have been all but abandoned. However, both approaches are basically flawed because both relativity and the quantum theory are incomplete as they now stand. Had either side of the quantum versus relativity controversy just simplified their worldview and sought commonality between the two, unification would have been accomplished long ago. The point is, literally, that the discrete quantum, continuous relativity, basic physical geometry and classical physics all share one common characteristic – a paradoxical duality between a dimensionless point (discrete) and an extended length (continuity) in any dimension – and if the problem of unification is approached from an understanding of how this paradox relates to each paradigm all of physics could be unified under a single new theoretical paradigm. Unfortunately there has never been a method, either mathematical or physical, by which a three-dimensional space can be generated from two or more dimensionless points. This shortcoming raises the question – how can the dimensionless point-particles of the Standard Model which presently dominates physics be extended to account for the three-dimensional space in which the physical interactions they describe occur? Fortunately, this question can now be answered, but the answer does not favor the Standard Model of the quantum as it is presently interpreted. Instead, a unified field theory based on continuity that completely unifies the quantum and relativity and completely incorporates the Standard Model as well as the Superstring, Brane and commonly accepted classical theories has been completed.

I have previously presented a geometrical explanation of Dark Matter and Dark Energy that is falsifiable, but the model was criticized for being non-mathematical. In this structure, the four-dimensional space-time of relativity is extrinsically curved in a higher spatial dimension. Dark Matter is curvature in the higher dimension that is not directly associated with local matter, but instead results from an interaction between the curvature of local matter and the global curvature due to all matter in the universe. The earlier criticism has now been overcome by looking at the possible particulate source of galactic halos and a simple yet revolutionary algebraic formula has been derived. The algebraic formula implies a five-dimensional unified field structure such as that developed by Kaluza in 1921 and extended by Einstein and his colleagues in the late 1930s. Others, such a H.T. Flint, have developed
more complete mathematical models of similar five-dimensional structures. The new equation also shows how gravity can be quantized on the basis of relativity without hypothesizing the discrete nature of matter, i.e., the existence of specific ‘particles’ of gravity, inherent in quantum mechanics, the Standard Model and other quantum models.

In this research thesis, (part II), we analyze Further equations related to Karatsuba's study of Riemann's zeta function We describe the possible mathematical connections and applications to the some sectors of String Theory, String Cosmology and Ramanujan Mathematics..

In the present research thesis, we have obtained further interesting new possible mathematical connections concerning the mathematics of Ramanujan mock theta functions, some sectors of Particle Physics, concerning principally the Dark Matter candidate particles and the physics of black holes. Furthermore, we have described a new possible Theory of Mathematical Connections between some Ramanujan's equations and Approximations to π, the equations of Inflationary Cosmology concerning the scalar field , the Inflaton mass, the Higgs boson mass and the Pion meson ± mass. In conclusion, we have analyzed a fundamental modular equation for an initial theoretical framework concerning the motivations of the mathematical connections that are obtained between various formulas of Ramanujan's mathematics and different parameters of Theoretical Physics and Cosmology


v2 -  UPDATED AND REVISITED VERSION    16.03.2021

In this paper we have described several Ramanujan's expressions and obtained some mathematical connections with various equations concerning different sectors of Cosmology and Black Holes/Wormholes Physics.

REVISITED AND DEFINITIVE VERSION  13.12.2020