On Some Mathematical Connections between the Cyclic Universe, Inflationary Universe, p-Adic Inflation, p-Adic Cosmology and Various Sectors of Number Theory

This paper is a review, a thesis, of some interesting results that have been obtained in various research concerning the “brane collisions in string and M-theory” (Cyclic Universe), p-adic inflation and p-adic cosmology. In Section 2, we have described some equations concerning cosmic evolution in a Cyclic Universe. In Section 3, we have described some equations concerning the cosmological perturbations in a Big Crunch/Big Bang space-time, the M-theory model of a Big Crunch/Big Bang transition and some equations concerning the solution of a braneworld Big Crunch/Big Bang Cosmology. In Section 4, we have described some equations concerning the generating ekpyrotic curvature perturbations before the Big Bang, some equations concerning the effective five-dimensional theory of the strongly coupled heterotic string as a gauged version of N=1five-dimensional supergravity with four-dimensional boundaries, and some equations concerning the colliding branes and the origin of the Hot Big Bang. In Section 5, we have described some equations regarding the “null energy condition” violation concerning the inflationary models and some equations concerning the evolution to a smooth universe in an ekpyrotic contracting phase with w>1. In Section 6, we have described some equations concerning the approximate inflationary solutions rolling away from the unstable maximum of p-adic string theory. In Section 7, we have described various equations concerning the p-adic minisuperspace model, zeta strings, zeta nonlocal scalar fields and p-adic and adelic quantum cosmology. In Section 8, we have shown various and interesting mathematical connections between some equations concerning the p-adic inflation, the p-adic quantum cosmology, the zeta strings and the brane collisions in string and M-theory. Furthermore, in each section, we have shown the mathematical connections with various sectors of Number Theory, principally the Ramanujan’s modular equations, the Aurea Ratio and the Fibonacci’s numbers.

Cosmic String Theory: Gravity and Tension

Planets are interconnected via magnetic field lines, which allow flux transfer events. In this paper, a thought experiment is performed whereby the Sun and planets are visualized as a violin with magnetic field lines analogous to strings of the violin. Frequency calculations for vibrating strings between the Earth and Sun compare favorably with measured satellite data for flux transfer events. Ideal Schumann Resonance was calculated using speed of light, diameter of the Earth and Earth’s gravity for tension. The force of attraction and repulsion of magnets is analogous to tension and compression resulting from tremendously low frequency (TLF) electromechanical waves. Gravity waves are thus theorized as mechanical waves brought about by the tension of electron strings, which also act dually as electromagnetic waves. Future harmonic analysis of flux transfer wave forms for each planet would add credence to the string theory as the theory of everything.

Doppler’s Effect, Gravity and Cosmology

We first show that Doppler’s effect implies that the time runs identically in the frames of reference of the source of light and the observer. Furthermore, we then show that the frequency shift due to the (assumed) expansion of space, if any, is “indistinguishable” from that due to the motion of the source with respect to the observer;and that the shift does not depend on the distance to the source. Observed frequency shifts of cosmological sources then need to be interpreted as being only due to their motions with respect to us. This has important implications for our ideas in cosmology.

New Concept of Physics Energy Behaviour and Its Application in Cosmology to Define Gravity Value from Einstein’s Relativity

The goal is to define Quantum Gravity Value by combination between our new concept about physics energy behaviour [1] and Einstein relativity’s Theory [2]. Our theory is based on the existence of a relationship between energy and vacuum! So it can be considered that the energy is a function of the vacuum ratio (v). Therefore, we can say that vacuum ratio constitutes a part of space-time. With simple mathematical formula, we can easily obtain the equation of the Energy Vacuum. This gives us the distribution of the energy Vacuum (E) into two parts are inversely proportional from our vacuum energy diagram, the effective energy that the sole responsible for Curvature of space-time fabric, and the lost energy that the responsible of the Gravitational waves [3]. From these equations, we can find that the relationship with Energy and Vacuum ratio is linear which are compatible with Quantum Mechanics laws and Maintains the energy conservation principle. It is also observed that the equations obtained through our theory are Combining relativity and Quantum Mechanics into one continuum. If we take the equations of our theory, we can easily obtain from Curvature of Space-Time Fabric, the Gravity value equation which equals to the square root of energy multiply times the square of the vacuum ratio. On other hand, a curvature matrix and a Time Dilation’s Circle are proposed, which gives us a new method to facilitate the calculations of the parameters involved in the Space-Time Curvature.

Derivation of Multiverse from Universal Wave Function Interpretation of String Theory

The multiverse is a hypothesis created to solve certain problems in cosmology. Currently, this scheme is still largely ad hoc, rather than derived from fundamental laws and principles. Because of this, the predictive power of this theory is rather limited. Furthermore, there are concerns that this theory will make it impossible to calculate some measured quantities, such as the masses of quarks and the electron. In this paper, we will show that a new development in string theory, the universal wave function interpretation of string theory, provides a way to derive the mathematical expression of the multiverse. We will demonstrate that the Weyl invariance existing in string theory indicates that our observed universe is a projection from a hologram. We will present how the laws of physics can be derived from this fact. Furthermore, we suggest it may also provide a way to calculate the masses of fundamental particles such as quarks and the electron.

What Gravity Is: Alzofon-Ionescu Theory beyond Newton, Einstein, Quantum/Entropy Gravity, etc. A Virequest Project Proposal

Gravity is not a fundamental force;in a nut-shell, it is the result of a non-commutative interaction of the “electric” (i.e. Coulomb type) due to fractional charges of the proton and neutron in U(2)-gauge theory, but which have no structure in U(1)-gauge theory, being neutral in itself (neutron), or when compensated by the electronic cloud (proton). This is no longer true at the SU(2) Electroweak Theory level, once spherical 3D-symmetry is broken to a finite Platonic group of symmetry within it Γ → SU(2). The fine splitting of energy levels due to the quark structure (frame basis in SU(2)) of the electric charge can be experimentally controlled using a MASER to invert the population and orient the nuclei the right way to reduce and turn off Gravity.

The Electromagnetic Nature of Gravitation and Matter-Antimatter Antigravity. Surmise on Quantum Vacuum Gravitation and Cosmology

We show that the electromagnetic quantum vacuum derives directly from Maxwell’s theory and plays a primary role in quantum electrodynamics, particle physics, gravitation and cosmology. It corresponds to the electromagnetic field ground state at zero frequency, a zero-energy cosmic field permeating all of space and it is composed of real states, called kenons (κενο = vacuum). Photons are local oscillations of kenons guided by a non-local vector potential wave function with quantized amplitude. They propagate at the speed imposed by the vacuum electric permittivity ε0 and magnetic permeability μ0, which are intrinsic properties of the electromagnetic quantum vacuum. The electron-positron elementary charge derives naturally from the electromagnetic quantum vacuum and is related to the photon vector potential. We establish the masse-charge equivalence relation showing that the masses of all particles (leptons, mesons, baryons) and antiparticles are states of the elementary charges and their magnetic moments. The equivalence between Newton’s gravitational law and Coulomb’s electrostatic law results naturally. In addition, we show that the gravitational constant G is expressed explicitly through the electromagnetic quantum vacuum constants putting in evidence the electromagnetic nature of gravity. We draw that G is the same for matter and antimatter but gravitational forces should be repulsive between particles and antiparticles because their masses bear naturally opposite signs. The electromagnetic quantum vacuum appears to be the natural link between quantum electrodynamics, particle physics, gravitation and cosmology and constitutes a basic step towards a unified field theory. Dark Energy and Dark Matter might originate from the electromagnetic quantum vacuum fluctuations. The calculated electromagnetic vacuum energy density, related to the cosmological constant considered responsible for the cosmic acceleration, is in good agreement with the astrophysical observations. The cosmic acceleration may be due to both “quantum vacuum fluctuations” and “matter-antimatter gravitational repelling”. All the above results are established without stating any assumptions or postulates. Next, we advance two hypotheses with cosmological impact. The first is based on the possibility that gravitation is due to the electromagnetic quantum vacuum density of states fluctuations giving rise to a photon pressure at the characteristic collective oscillation frequencies of the charge densities composing the bodies (Electromagnetic Push Gravity). The second advances that energy, matter and antimatter in the universe emerge spontaneously from the quantum vacuum fluctuations as residues that remain stable in space and we present the main principles upon which a new cosmological model may be developed overcoming the well-known Big Bang issues.

The bulk viscous string cosmology in an anisotropic universe with late time acceleration

A model of a cloud formed by massive strings is used as a source of Bianchi type II cases. We assume that the expansion （θ） in the model is proportional to the shear （σ）. To get an exact solution, we consider the equation of state of the fluid to be in the stiff form. It is found that the bulk viscosity played a very important role in the history of the universe. In the presence of bulk viscosity the particles dominate over strings whereas in the absence of it, strings dominate over the particles, which is not consistent with recent observations. Also we observe that the viscosity causes the expansion of the universe to be accelerating. Our models are evolving from an early decelerating phase to a late time accelerating phase. The physical and geometrical behaviors of these models are discussed.

The Reversible Cyclic Universe in the Reversible Multiverse and the Reversible String Theory

The paper posits that the multiverse is reversible, so all universes in the multiverse are reversible cyclic universes which have the inexhaustible resources of space-time to expand. The collision of expanding universes is permanently irreversible, forbidden in the reversible multiverse, so every universe is surrounded by the zero-energy interuniversal void as the permanent gap among universes to keep universes apart. A zero-sum energy dual universe of positive energy universe and negative energy universe can be created in the interuniversal void, and the new dual universe is again surrounded by the interuniversal void. This paper also posits the reversible string theory with oscillating space-time dimension number oscillating between 11D (space-time dimension) and 4D without the conventional compactization of string. Dimension number decreases with decreasing speed of light, decreasing vacuum energy, and increasing rest mass. The 4D and the 11D have zero and the highest vacuum energies, respectively. The universes in the reversible multiverse oscillate reversibly between high and low dimension numbers. Under symmetry breaking as in our universe, the positive energy universe as our observed universe absorbed the interuniversal void, while the negative energy universe did not. The interuniversal void has zero vacuum energy, so the absorption of the interuniversal void by the positive energy universe forced the positive energy 10D universe with high vacuum energy to be transformed into the positive energy 4D universe with zero vacuum energy, resulting in the inflation followed by the Big Bang. The negative energy universe undergoes dimension number oscillation between 4D and 10D dimension by dimension. The negative energy >4D universe is hidden, and the negative energy 4D universe appears as dark energy. The calculated percentages of dark energy, dark matter, and baryonic matter and the calculated time for dark energy to start are in good agreements with the observed values.

String Theory with Oscillating Space-Time Dimension Number

In conventional string theory with fixed space-time dimension number, the extra space dimensions are compactized. In string theory with oscillating space-time dimension number, dimension number oscillates between 11D and 10D and between 10D and 4D reversibly, and there is no compactization. Dimension number decreases with decreasing speed of light and increasing rest mass. The 4D particle has the lowest speed of light and the highest rest mass. The two different oscillations between 10D and 4D are the stepwise oscillation passing through every dimension number and the direct oscillation oscillating directly between 10D and 4D without the intermediate dimension numbers. Dark energy represents the stepwise oscillation, and dark energy becomes observable only when it has 4D space-time. 4D baryonic matter and 4D dark matter represent the direct oscillation directly from 10D to 4D. Our universe is the dual cyclic universe of the dark energy universe and the baryonic-dark matter universe. The Big Bang in the baryonicdark matter universe produced irreversible kinetic energy that stopped the reversible direct oscillation. The reversible direct oscillation will resume after the Big Crush to remove irreversible kinetic energy. Our cyclic universe started from the zero-energy universe through the four-stage transformation. The theoretical calculated percentages of dark energy, dark matter, and baryonic matter are 68.3, 26.4, and 5.3, respectively, in agreement with observed 68.3, 26.8, and 4.9, respectively. According to the calculation, dark energy started in 4.28 billion years ago in agreement with the observed 4.71 ± 0.98 billion years ago.

Unification of Gravity and Electromagnetism

Gravity and electromagnetism are two sides of the same coin, which is the clue of this unification. Gravity and electromagnetism are represented by two mathematical structures, symmetric and antisymmetric respectively. Einstein gravitational field equation is the symmetric mathematical structure. Electrodynamics Lagrangian is three parts, for electromagnetic field, Dirac field and interaction term. The definition of canonical energy momentum tensor was used for each term in Electrodynamics Lagrangian to construct the antisymmetric mathematical structure; symmetric and antisymmetric gravitational field equations are two sides of the same Lagrangian.

The Many Faces of Gravity

We show that the number of different gravitational effects is significantly greater than previously thought. First of all, it turned out that the observed constancy of the speed of light relative to the surrounding masses is a special case of a previously unknown fundamental gravitational effect related to the action of gravitation on the speed of light. In other words, the constancy of the speed of light becomes an integral part of gravitation. Moreover, it turned out that the increase in inertial mass and the dilation of the proper time of particles that were accelerated relative to the surrounding masses are also consequences of this fundamental gravitational effect. All of these secondary effects are in the same row with such well-known effects as gravitational refraction and gravitational lensing, which are also a consequence of the action of gravitation on the speed of light. Their belonging to gravitation causes a number of unique features, for example, asymmetry in time dilation and anisotropy of the speed of light, which have been successfully confirmed experimentally. The research is based on a detailed analysis of a large set of experimental data using the classical axiomatic approach.

Negative corrections to black hole entropy from string theory

We report for the first time that in heterotic string compactified on 4-torus or equivalently IIA string compactified on K3,the leading α′corrections to the rotating black string entropy at fixed conserved charges can be negative.This further implies that the correction to the mass of extremal rotating string is positive,opposite to the standard expectation from the weak gravity conjecture.Our result suggests that the validity of positivity of entropy shift due to higher order operators depends on other factors omitted previously in the effective field theory analysis.

Split Membrane 11D Spacetime = 1D Eleventh Dimension Interval Space + 6D Rishon Space + 3D Higgs Space + 1D Einstein Time: Cosmology

The paper posits that the cyclic universe cosmology involves the split of the membrane 11D (11 dimensional) spacetime into the 1D eleventh dimension orbifold interval space to form gravity, the 6D discrete interior rishon space (TTT-VVV for positron-neutrino or TTV-TVV for?quarks) to form the Standard Model, the 3D Higgs space (attachment space to attach matter or detachment space to detach matter) to form the Higgs or reverse Higgs field, and 1D Einstein time to be shared by all spaces. To establish particle masses, spacetime dimension number decreases with decreasing speed of light, decreasing vacuum energy, and increasing rest mass. The 4D and the 10D have zero and the highest vacuum energies, respectively. The cyclic universe cosmology starts with the zero-energy 4D inter-universal void and the positive-energy membrane and negative-energy antimembrane 11D dual universe which is split into four equal 10D string branes, including the 10D positive-energy weak-gravity brane with matter, negative-energy strong-gravity brane, negative-energy weak-gravity brane with antimatter, and positive-energy strong-gravity brane in the 11D bulk with the 1D eleventh dimension interval space in between the strong and the weak-gravity branes. To form the home universe where we inhabit, the 10D positive-energy weak-gravity brane with attachment space absorbed the zero-energy 4D inter-universal void with detachment space, resulting in the combination of rest mass from attachment space and kinetic energy from detachment space, the formation of the 4D spacetime universe by transforming 6D connected exterior space into 6D discrete interior rishon space, and cosmic inflation. The other three branes did not absorb the inter-universal void, resulting in the oscillating dimension branes between 10D and 4D stepwise without kinetic energy. The three branes are hidden when D > 4, and they are dark energy when D = 4. The split 11D spacetime and cosmology provide the matter-antimatter imbalance and the accurately calculated masses for leptons, quarks, hadrons, gauge bosons, the Higgs boson, gravity, dark matter, and dark energy.

Clues to the Fundamental Nature of Gravity, Dark Energy and Dark Matter

This paper integrates the Flat Space Cosmology (FSC) model into the Friedmann equations containing a cosmological term. The Lambda term within this model scales according to 3H2t/c2 and 3/R2t. Use of the Bekenstein-Hawking definition of closed gravitational system total entropy provides for FSC cosmic parameter definitions in terms of . Cosmic time, radius, total matter mass-energy and vacuum energy in this model scale in exactly the same way as . This analysis opens the way for understanding gravity, dark energy and dark matter as being deeply connected with cosmic entropy. The recent theoretical work of Roger Penrose and Erik Verlinde is discussed in this context. The results of this FSC model analysis dovetail nicely with Verlinde’s work suggesting gravity as being fundamentally an emergent property of cosmic entropy. This emergent-property-of-entropy definition of gravity, if true, would also indicate that gravitational inertia, dark matter and dark energy are simply manifestations of cosmic entropy. Thus, they would likely have no identifiable connection to quantum physics, including the standard particle model.

Why Flat Space Cosmology Is Superior to Standard Inflationary Cosmology

Following recent Cosmic Microwave Background (CMB) observations of global spatial flatness, only two types of viable cosmological models remain: inflationary models which almost instantaneously attain cosmic flatness following the Big Bang;and non-inflationary models which are spatially flat from inception. Flat Space Cosmology (FSC) is the latter type of cosmological model by virtue of assumptions corresponding to the Hawking-Penrose conjecture that a universe expanding from a singularity could be modeled like a time-reversed black hole. Since current inflationary models have been criticized for their lack of falsifiability, the numerous falsifiable predictions and key features of the FSC model are herein contrasted with standard inflationary cosmology. For the reasons given, the FSC model is shown to be superior to standard cosmology in the following eleven categories: Predictions Pertaining to Primordial Gravity Waves;Cosmic Dawn Early Surprises;Predicting the Magnitude of CMB Temperature Anisotropy;Predicting the Value of Equation of State Term w;Predicting the Hubble Parameter Value;Quantifiable Entropy and the Entropic Arrow of Time;Clues to the Nature of Gravity, Dark Energy and Dark Matter;The Cosmological Constant Problem;Quantum Cosmology;Dark Matter and Dark Energy Quantitation;Requirements for New Physics.

Spatial covariant gravity with two degrees of freedom in the presence of an auxiliary scalar field:Perturbation analysis

We investigate a class of gravity theories respecting only spatial covariance,termed spatially covariant gravity,in the presence of an auxiliary scalar field.We examine the conditions on the Lagrangian required to eliminate scalar degrees of freedom,allowing only two tensorial degrees of freedom to propagate.Instead of strict constraint analysis,in this paper,we employ the perturbation method and focus on the necessary conditions to evade the scalar mode at the linear order in perturbations around a cosmological background.Beginning with a general action and solving the auxiliary perturbation variables in terms of a would-be dynamical scalar mode,we derive the condition to remove its kinetic term,thus ensuring that no scalar mode propagates.As an application of the general condition,we study a polynomial-type Lagrangian as a concrete example,in which all monomials are spatially covariant scalars containing two derivatives.We find that the auxiliary scalar field is essential,and new terms in the Lagrangian are allowed.Our analysis provides insights into constructing gravity theories with two degrees of freedom in the extended framework of spatially covariant gravity.

Thermodynamics of 4D dS/AdS Gauss–Bonnet black holes according to consistent gravity theory in the presence of a cloud of strings

By looking at the Lovelock theorem one can infer that the gravity model given by[1]cannot be applicable for all types of 4D Einstein–Gauss–Bonnet(EGB)curved space-time.The reason for this is that in 4D space-time,the Gauss–Bonnet invariant is a total derivative and hence it does not contribute to gravitational dynamics.Hence,the authors of[2]presented an alternative consistent EGB gravity model instead of[1]by applying a break-of-diffeomorphism property.In this work,we use the alternative model to produce a de Sitter(dS)/Anti-de Sitter(AdS)black hole metric and then investigate its thermodynamic behavior in the presence of a cloud of Nambu–Goto strings.Mathematical derivations show that the resulting diagrams of pressure vs specific volume at a constant temperature are similar to that for a van der Waals gas/fluid in an ordinary thermodynamic system in the d S sector but not in the Ad S background.From this,we infer that the black hole participates in the small-to-large black hole phase transition in the dS background,while it exhibits a Hawking–Page phase transition in the AdS background.In the latter case,an evaporating black hole eventually reaches an AdS vacuum space because of its instability.

Cloud of strings in f(R) gravity

We derive the solution for a spherically symmetric string cloud configuration in a ＆dimensional spacetime in the framework of f（R） theories of gravity. We also analyze some thermodynamic properties of the joint black hole - cloud of strings solution. For its Hawking temperature, we found that the dependence of the mass with the horizon is significantly different in both theories. For the interaction of a black hole with thermal radiation, we found that the shapes of the curves are similar, but shifted. Our analysis generalizes some known results in the literature.

Physical aspects of f(R,G_(μν)T^(μν))modified gravity theories

The paper extends basic Einstein–Hilbert action by incorporating an invariant derived from a specific contraction between the Einstein tensor and energy momentum tensor.This represents a non–minimal coupling between the space–time geometry and matter fields.The fundamental Einstein–Hilbert action is extended by considering a generic function f(R,GμνTμν).This function is subsequently dissected into its primary components:a geometric part reliant on the scalar curvature,and another segment encapsulating the interaction between geometry and matter fields.Distinct cosmological models are formulated at the backdrop of these dynamics,rooted in specific associations between the matter energy-momentum tensor and Einstein tensor.Upon deriving the consequent field equations,the cosmological model's physical implications are explored through a dynamical system analysis applied to diverse coupling functions.This exploration reveals that the current model aligns with various phases in the Universe's evolution,potentially elucidating several late-time historical epochs.