Modified theories of Gravity Research Papers (original) (raw)

Motivated by the lack of rotating solutions sourced by matter in General Relativity as well as in modified gravity theories, we extend a recently discovered exact rotating solution of the minimal Einstein-scalar theory to its counterpart... more

Motivated by the lack of rotating solutions sourced by matter in General Relativity as well as in modified gravity theories, we extend a recently discovered exact rotating solution of the minimal Einstein-scalar theory to its counterpart in Eddington-inspired Born-Infeld gravity coupled to a Born-Infeld scalar field. This is accomplished with the implementation of a well-developed mapping between solutions of Ricci-Based Palatini theories of gravity and General Relativity. The new solution is parametrized by the scalar charge and the Born-Infeld coupling constant apart from the mass and spin of the compact object. Compared to the spacetime prior to the mapping, we find that the high-energy modifications at the Born-Infeld scale are able to suppress but not remove the curvature divergence of the original naked null singularity. Depending on the sign of the Born-Infeld coupling constant, these modifications may even give rise to an additional timelike singularity exterior to the null ...

In this work we present the foundations of generalized scalar-tensor theories arising from vector bundle constructions, and we study the kinematic, dynamical and cosmological consequences. In particular, over a pseudo-Riemannian... more

In this work we present the foundations of generalized scalar-tensor theories arising from vector bundle constructions, and we study the kinematic, dynamical and cosmological consequences. In particular, over a pseudo-Riemannian space-time base manifold, we define a fiber structure with two scalar fields. The resulting space is a 6-dimensional vector bundle endowed with a non-linear connection. We provide the form of the geodesics and the Raychaudhuri and general field equations, both in Palatini and metrical method. When applied at a cosmological framework, this novel geometrical structure induces extra terms in the modified Friedmann equations, leading to the appearance of an effective dark energy sector, as well as of an interaction of the dark mater sector with the metric. We show that we can obtain the standard thermal history of the universe, with the sequence of matter and dark-energy epochs, and furthermore the effective dark-energy equation-of-state parameter can lie in the...

In this work we recover an abandoned line of research: the study of the gravitational interaction in the context of the Special Theory of Relativity. It is found that, as long as the equivalence principle is respected, a relativistic... more

In this work we recover an abandoned line of research: the study of the gravitational interaction in the context of the Special Theory of Relativity. It is found that, as long as the equivalence principle is respected, a relativistic non-linear energy conservation theorem arises in a natural way. We interpret that this non-linear conservation law stresses the non-linear character of the gravitational interaction.The theorem naturally reproduces the energy conservation theorem of Newtonian mechanics in the corresponding low energy limit, but also allows to derive some standard results of General Relativity, such as the formula of the gravitational redshift. In addition, the model can also provide some new aspects and predictions. In particular, it seems to implement the Mach principle in a natural way,a principle that is not included in the standard formulation of General Relativity. We also show that the escape velocity for an arbitrary particle at the Schwarzschild radius of a gravitational source is predicted to be lower than the speed of light, Vescapprox0,8cV_{esc}\approx0,8cVescapprox0,8c.

In the natural world, light and gravity are two widely prevalent and significant phenomena. They not only provide humans with rich information about the universe but also play important roles in scientific research. Although light and... more

In the natural world, light and gravity are two widely prevalent and significant phenomena. They not only provide humans with rich information about the universe but also play important roles in scientific research. Although light and gravity may not appear to have a direct connection on the surface, can we find a correlation between them? The discovery of gravitational waves provides us with new clues. The LIGO gravitational wave detection experiment successfully detected gravitational waves, which are believed to be caused by disturbances in the gravitational field and propagate at the speed of light. This raises an intriguing question: do light and gravitational waves share a medium for energy transmission? Furthermore, can we establish a unified physical model to explain the physical mechanisms of electric fields, magnetic fields, and gravitational fields, as well as their relationships? This study focuses on these questions, thoroughly analyzes the phenomena of light and gravity, and ultimately establishes a unified field theory framework to comprehensively understand the fundamental matter and energy in the universe. Unified field theory under the same physical model also establishes a theoretical basis for how to overcome gravity.

Contents: Review of conservation laws in GR from both mathematical and physical perspective; maximally symmetric spacetimes; Noether theorem in GR; KBL superpotential and its generalization to modified gravity; Horndeski theory and... more

Contents: Review of conservation laws in GR from both mathematical and physical perspective; maximally symmetric spacetimes; Noether theorem in GR; KBL superpotential and its generalization to modified gravity; Horndeski theory and construction of superpotentials for spacetimes representing black holes and cosmological models;

Since Einstein died in 1955, very few theoretical scientists have tried to complete his work because the pendulum of history has swung toward favoring field theories based on the quantum for the expected unification of physics. Nearly... more

Since Einstein died in 1955, very few theoretical scientists have tried to complete his work because the pendulum of history has swung toward favoring field theories based on the quantum for the expected unification of physics. Nearly everyone now believes that the quantum (discrete point) and relativity (continuity) are incompatible and the quantum is more fundamental than relativity and continuity, so those who have sought unification have looked for new and unique quantum approaches to accomplish unification. However, the truth is that the quantum and relativity are not incompatible and the traditional differences between the two–discreteness and continuity, indeterminism and determinism–are just the outward appearances of an even deeper fundamental problem–geometric point and extension–that when solved renders relativity and the quantum completely compatible. This deeper problem is even more significant because Riemann knew of and failed to consider and even purposely ignored the problem of point-elements and based his differential geometry of surfaces on metric-elements alone. Therefore, expanding the Riemannian geometry to include point-elements, which can be interpreted as discrete points for the quantum, forms a fundamental enough foundation for developing a unified field theory.

This Thesis is devoted to the study of phenomenologically viable gravitational theories, in order to address the most pressing open issues both at very small and very large energy scales. Lovelock’s theorem singles out General Relativity... more

This Thesis is devoted to the study of phenomenologically viable gravitational theories, in order to address the most pressing open issues both at very small and very large energy
scales. Lovelock’s theorem singles out General Relativity as the only theory with second-order field equations for the metric tensor. So, two possible ways to circumvent it and
modify the gravitational sector are taken into account. The first route consists in giving up diffeomorphism invariance, which generically leads to extra propagating degrees of
freedom. In this framework Horava gravity is discussed, presenting two restrictions, called respectively “projectability” and “detailed balance”, which are imposed in order to reduce
the number of terms in the full theory. We introduce a new version of the theory assuming detailed balance but not projectability, and we show that such theory is dynamically
consistent as both the spin-0 and spin-2 gravitons have a well behaved dynamics at lowenergy. Moreover three-dimensional rotating black hole solutions are found and fully studied in the context of Horava gravity, shedding light on its causal structure. A new concept of black hole horizon, dubbed “universal horizon”, arises besides the usual event horizon one, since in Lorentz-violating gravity theories there can be modes propagating even at infinite speed. The second route which is considered, consists in adding extra fields to the gravitational action while diffeomorphism invariance is preserved. In this respect we consider the less explored option that such fields are auxiliary fields, so they do not satisfy dynamical equations but can be instead algebraically eliminated. A very general parametrization for these theories is constructed, rendering also possible to put on them very tight, theory-independent constraints. Some insight about the cosmological implications of such theories is also given. Finally in the conclusions we discuss about the future challenges that the aforementioned gravity theories have to face.

After general relativity and quantum mechanics were generally accepted, it was thought that grand unification and the theory of everything could not be far off. Yet, the struggle to find the theory of everything persisted over the past... more

After general relativity and quantum mechanics were generally accepted, it was thought that grand unification and the theory of everything could not be far off. Yet, the struggle to find the theory of everything persisted over the past 100 years. Why this theory has been so elusive is easy to see in hindsight and the top 10 reasons are listed.

The unified field dynamics of gravitational mass-ENERGY-Matter - uniting Newtonian and relativistic gravity theories through equilateral Planck quanta to reveal the trifold force interactions that create universal gravitation between... more

The unified field dynamics of gravitational mass-ENERGY-Matter - uniting Newtonian and relativistic gravity theories through equilateral Planck quanta to reveal the trifold force interactions that create universal gravitation between material objects - and a corrected model of stellar fusion.

This book presents a new approach to Relativity Theory (RT) and Quantum Mechanics (QM). The main motivation for this work is that RT and QM appear to be incompatible with one another. In addition, a number of physically important cases... more

This book presents a new approach to Relativity Theory (RT) and Quantum Mechanics (QM). The main motivation for this work is that RT and QM appear to be incompatible with one another. In addition, a number of physically important cases and well-documented experiments cannot be ex-plained within the framework of those two theories.

Over the past decades, General Relativity and the concordance ΛCDM model have been successfully tested using several different astrophysical and cosmological probes based on large datasets ({\it precision cosmology}). Despite their... more

Over the past decades, General Relativity and the concordance ΛCDM model have been successfully tested using several different astrophysical and cosmological probes based on large datasets ({\it precision cosmology}). Despite their successes, some shortcomings emerge due to the fact that General Relativity should be revised at infrared and ultraviolet limits and to the fact that the fundamental nature of Dark Matter and Dark Energy is still a puzzle to be solved. In this perspective, f(R) gravity have been extensively investigated being the most straightforward way to modify General Relativity and to overcame some of the above shortcomings. In this paper, we review various aspects of f(R) gravity at extragalactic and cosmological levels. In particular, we consider cluster of galaxies, cosmological perturbations, and N-Body simulations, focusing on those models that satisfy both cosmological and local gravity constraints. The perspective is that some classes of f(R) models can be consistently constrained by Large Scale Structure.

The Schwarzschild–de Sitter (SdS) solution exists in the large majority of modified gravity theories, as expected, and in particular the effective cosmological constant is determined by the specific parameters of the given theory. We... more

The Schwarzschild–de Sitter (SdS) solution exists in the large majority of modified gravity theories, as expected, and in particular the effective cosmological constant is determined by the specific parameters of the given theory. We explore the possibility to use future extended radio-tracking data from the currently ongoing New Horizons mission in the outskirts peripheries of the Solar System, at about 40 au, in order to constrain this effective cosmological constant, and thus to impose constrain on each scenario's parameters. We investigate some of the recently most studied modified gravities, namely f (R) and f (T) theories, dRGT massive gravity, and Hořava–Lifshitz gravity, and we show that New Horizons mission may bring an improvement of one-two orders of magnitude with respect to the present bounds from planetary orbital dynamics.

There is a distinct possibility that current and future cosmological data can be used to constrain Einstein's theory of gravity on the very largest scales. To be able to do this in a model-independent way, it makes sense to work with a... more

There is a distinct possibility that current and future cosmological data can be used to constrain Einstein's theory of gravity on the very largest scales. To be able to do this in a model-independent way, it makes sense to work with a general parameterization of modified gravity. Such an approach would be analogous to the Parameterized Post-Newtonian (PPN) approach which is used on the scale of the Solar System. A few such parameterizations have been proposed and preliminary constraints have been obtained. We show that the majority of such parameterizations are only exactly applicable in the quasistatic regime. On larger scales they fail to encapsulate the full behaviour of typical models currently under consideration. We suggest that it may be possible to capture the additions to the `Parameterized Post-Friedmann' (PPF) formalism by treating them akin to fluid perturbations.

This paper by William S. Alek deserves serious attention. It explores concepts related to "Free Energy" and the control of Gravity/Antigravity that are based entirely within the framework of extended classical Newtonian physics called... more

This paper by William S. Alek deserves serious attention. It explores concepts related to "Free Energy" and the control of Gravity/Antigravity that are based entirely within the framework of extended classical Newtonian physics called Newtonian Torsion Physics. It is shown that the cause of gravity is a type of macroscopic torque between inertial frames where the origin of the torque occurs within imaginary or complex space. The effect manifests in real space as universal mass attraction, or gravity. A correlation has been discovered between mass, inductors, and capacitors, thereby relating the imaginary or complex origin of torque to gravity, and how this same torque affects electromagnetism.

This study illustrates why it is physically impossible that LIGO's interferometers can really detect motions whose order of magnitude should be – as expected-10-19 meters (1/10,000 the size of a proton). And finally it shows why gravity –... more

This study illustrates why it is physically impossible that LIGO's interferometers can really detect motions whose order of magnitude should be – as expected-10-19 meters (1/10,000 the size of a proton). And finally it shows why gravity – as linked to the universal inertia according to the Mach's Principle-does not need any wave/energy to instantaneously synchronize.

In this work, we have developed an elegant algorithm to study the cosmological consequences from a huge class of quantum field theories (i.e. superstring theory, supergrav-ity, extra dimensional theory, modified gravity etc.), which are... more

In this work, we have developed an elegant algorithm to study the cosmological consequences from a huge class of quantum field theories (i.e. superstring theory, supergrav-ity, extra dimensional theory, modified gravity etc.), which are equivalently described by soft attractors in the effective field theory framework. In this description we have restricted our analysis for two scalar fields-dilaton and Higgsotic fields minimally coupled with Einstein gravity, which can be generalized for any arbitrary number of scalar field contents with generalized non-canonical and non-minimal interactions. We have explicitly used R 2 gravity, from which we have studied the attractor and non-attractor phase by exactly computing two point, three point and four point correlation functions from scalar fluctuations using In-In (Schwinger-Keldysh) and δN formalism. We have also presented theoretical bounds on the amplitude, tilt and running of the primordial power spectrum, various shapes (equilateral, squeezed, folded kite or counter collinear) of the amplitude as obtained from three and four point scalar functions, which are consistent with observed data. Also the results from two point tensor fluctuations and field excursion formula are explicitly presented for attractor and non-attractor phase. Further, reheating constraints, scale dependent behaviour of the couplings and the dynamical solution for the dilaton and Higgsotic fields are also presented. New sets of consistency relations between two, three and four point observables are also presented, which shows significant deviation from canonical slow roll models. Additionally, three possible theoretical proposals have presented to overcome the tachyonic instability at the time of late time acceleration. Finally, we have also provided the bulk interpretation from the three and four point scalar correlation functions for completeness.

Now, for the first time astronomers have directly imaged the last piece of the puzzle that ties them all together – a dusty donut of material that surrounds a supermassive black hole. TORROIDS ARE FORMED IN THE AETHERS BY ANUs LINKING UP... more

Now, for the first time astronomers have directly imaged the last piece of the puzzle that ties them all together – a dusty donut of material that surrounds a supermassive black hole.
TORROIDS ARE FORMED IN THE AETHERS BY ANUs LINKING UP - TO MANIFEST GRAVITY, VIBRATIONS, LINEAL TIME, THE FIBONACCI SERIES, ALL OF THE PROPERTIES OF OUR 3D REALM ARE A FUNCTION OF TORROID FORMATION DUE TO THE RULE

We construct an updated and extended compilation of growth rate data consisting of 34 points and including corrections for model dependence. In order to maximize the independence of the datapoints we also construct a subsample of this... more

We construct an updated and extended compilation of growth rate data consisting of 34 points and including corrections for model dependence. In order to maximize the independence of the datapoints we also construct a subsample of this compilation (`Gold' growth dataset) which consists of 18 datapoints. We test the consistency of this dataset with the best fit Planck15/$\Lambda$CDM parameters in the context of General Relativity (GR) using the evolution equation for the growth factor delta(a)\delta(a)delta(a) with a wwwCDM background. We find tension at the sim3sigma\sim 3 \sigmasim3sigma level between the best fit parameters www (the dark energy equation of state), Omega0m\Omega_{0m}Omega0m (the matter density parameter) and sigma8\sigma_8sigma8 (the matter power spectrum normalization on scales 8h−18h^{-1}8h1Mpc) and the corresponding Planck15/$\Lambda$CDM parameters. We show that the tension disappears if we allow for evolution of the effective Newton's constant, parametrized as Geff(a)/GN=1+ga(1−a)n−ga(1−a)2nG_{eff}(a)/G_N = 1 + g_a(1-a)^n-g_a(1-a)^{2n}Geff(a)/GN=1+ga(1a)nga(1a)2n with nge2n\ge2nge2 where gag_aga, nnn are parameters of the model, aaa is the scale factor and z=1/a−1z = 1/a-1z=1/a1 is the redshift. This parametrization satisfies three criteria: a. Geff>0G_{eff} > 0Geff>0, b. Consistency with Big Bang Nucleosynthesis ($G_{eff}(a\ll 1)/G_N=1$), c. Consistency with solar system tests ($G_{eff}(a=1)/G_N=1$ and Geff′(a=1)/GN=0G_{eff}'(a=1)/G_N=0Geff(a=1)/GN=0). We show that the best fit form of Geff(z)G_{eff}(z)Geff(z) obtained from the growth data corresponds to weakening gravity at recent redshifts (decreasing function of zzz) and we demonstrate that this behavior is not consistent with any scalar-tensor Lagrangian with a real scalar field. Finally, we use MGCAMB to find the best fit Geff(z)G_{eff}(z)Geff(z) obtained from the Planck CMB power spectrum on large angular scales and show that it is a mildly increasing function of zzz, in 3sigma3\sigma3sigma tension with the corresponding decreasing best fit Geff(z)G_{eff}(z)Geff(z) obtained from the growth data.

A theory of everything , or, grand unified theory (which Einstein had been working on without success, with Superstring Theory now being a good candidate), is one which unites all the forces of nature, viz., gravity, electromagnetism, the... more

A theory of everything , or, grand unified theory (which Einstein had been working on without success, with Superstring Theory now being a good candidate), is one which unites all the forces of nature, viz., gravity, electromagnetism, the strong nuclear force and the weak nuclear force. Important as this theory might be, it is
lacking in one important fundamental aspect, viz., the role of consciousness, which could in fact be considered the most fundamental aspect of physics. This paper explains that a theory of consciousness is more important than a theory of everything or grand unified theory and should be the theory of everything instead, or, at least, a part of the theory of everything.

We propose a modified theory of gravitation constructed by the addition of the term f (Tµν T µν) to the Einstein-Hilbert action, and elaborate a particular case f (Tµν T µν) = α(Tµν T µν) η , where α and η are real constants, dubbed as... more

We propose a modified theory of gravitation constructed by the addition of the term f (Tµν T µν) to the Einstein-Hilbert action, and elaborate a particular case f (Tµν T µν) = α(Tµν T µν) η , where α and η are real constants, dubbed as energy-momentum powered gravity (EMPG). We search for viable cosmologies arising from EMPG especially in the context of the late-time accelerated expansion of the Universe. We investigate the ranges of the EMPG parameters (α, η) on theoretical as well as observational grounds leading to the late-time acceleration of the Universe with pressureless matter only, while keeping the successes of standard general relativity at early times. We find that η = 0 corresponds to the ΛCDM model, whereas η = 0 leads to a wCDM-type model. However, the underlying physics of the EMPG model is entirely different in the sense that the energy in the EMPG Universe is sourced by pressureless matter only. Moreover, the energy of the pressureless matter is not conserved, namely, in general it does not dilute as ρ ∝ a −3 with the expansion of the Universe. Finally, we constrain the parameters of an EMPG-based cosmology with a recent compilation of 28 Hubble parameter measurements, and find that this model describes an evolution of the Universe similar to that in the ΛCDM model. We briefly discuss that EMPG can be unified with Starobinsky gravity to describe the complete history of the Universe including the inflationary era.

The goal of this work is to elaborate on new geometric methods of constructing exact and parametric quasiperiodic solutions for anamorphic cosmology models in modified gravity theories, MGTs, and general relativity, GR. There exist... more

The goal of this work is to elaborate on new geometric methods of constructing exact and parametric quasiperiodic solutions for anamorphic cosmology models in modified gravity theories, MGTs, and general relativity, GR. There exist previously studied generic off-diagonal and diagonalizable cosmological metrics encoding gravitational and matter fields with quasicrystal like structures, QC, and holonomy corrections from loop quantum gravity, LQG. We apply the anholonomic frame deformation method, AFDM, in order to decouple the (modified) gravitational and matter field equations in general form. This allows us to find integral varieties of cosmological solutions determined by generating functions, effective sources, integration functions and constants. The coefficients of metrics and connections for such cosmological configurations depend, in general, on all spacetime coordinates and can be chosen to generate observable (quasi)-periodic/ aperiodic/ fractal / stochastic / (super) cluster / filament / polymer like (continuous, stochastic, fractal and/or discrete structures) in MGTs and/or GR. In this work, we study new classes of solutions for anamorphic cosmology with LQG holonomy corrections. Such solutions are characterized by nonlinear symmetries of generating functions for generic off–diagonal cosmological metrics and generalized connections, with possible nonholonomic constraints to Levi–Civita configurations and diagonalizable metrics depending only on a time like coordinate. We argue that anamorphic quasiperiodic cosmological models integrate the concept of quantum discrete spacetime, with certain gravitational QC-like vacuum and nonvacuum structures. And, that of a contracting universe that homogenizes, isotropizes and flattens without introducing initial conditions or multiverse problems.

We establish a dynamic effective model for explaining the accelerated expansion of the universe. The model is based on the quantum theory of gravity that predicts the existence of the negative gravitational charges. We show that the... more

We establish a dynamic effective model for explaining the accelerated expansion of the universe. The model is based on the quantum theory of gravity that predicts the existence of the negative gravitational charges. We show that the results of this model are equivalent to that of the dark energy models, and therefore, consistent with the observations. We suggest that the accelerated expansion of the universe is an observational evidence of the existence of the negative gravitational charges. This model predicts that the universe filled with negative gravitational charges is accelerated collapse. Moreover we propose an alternative physical interpretation that the cosmological constant is equivalent to the negative gravitational charges as a source of gravitational fields. This interpretation avoids the fine-tuning problem. This dynamic model predicts that the equation of state, the cosmological constant and the acceleration of the expansion of the universe are time dependent.

Книга посвящена ревизии основных взглядов современной физики. Она стала результатом 25 лет размышлений автора над этой проблемой. Автор дерз-нул усомниться не только в СТО и ОТО, но и в основах квантовой механики. Первая глава посвящена... more

Книга посвящена ревизии основных взглядов современной физики. Она стала результатом 25 лет размышлений автора над этой проблемой. Автор дерз-нул усомниться не только в СТО и ОТО, но и в основах квантовой механики.
Первая глава посвящена формулировке нового подхода к электродинамике. Предложены формулы для взаимодействия электрических зарядов, к которым пришли еще основоположники теории электричества, но которые, почему-то, не вошли в рассуждения современных теоретиков. Найдены так же соотношения, которые не рассматривались никогда ранее и требуют экспериментальной про-верки. В главе, посвященной гравитации, сделана попытка реализовать давнюю мечту ученых – объединить электричество и гравитацию. О ее успешности судить читателю. Для нового понимания термодинамики существенной оказалась необходимость пересмотреть траекторное представление о движении и ввести понятие поверхностной скорости, избежав стохастических манипуляций. По-добный подход позволяет детерминистски описать квантово-механические эф-фекты, ввести четкое понятие энтропии, которое оказалось краеугольным камнем для формулы Планка.
Книга рассчитана как на внимание людей, просто интересующихся наукой, так и профессиональных инженеров и физиков. Для понимания материала тре-буется подготовка на уровне курса высшей математики.

The most radical feature of General Relativity was its identification of gravity with spacetime curvature. However, in attempts to find a unified field theory, Einstein himself discovered an alternate way to look at gravity in which... more

The most radical feature of General Relativity was its identification of gravity with spacetime curvature. However, in attempts to find a unified field theory, Einstein himself discovered an alternate way to look at gravity in which spacetime was globally flat, but gravity was mediated by torsion. In this thesis, we will discuss two such theories of gravity which are equivalent to general relativity but build upon globally flat spacetime. The theories which will be discussed are Teleparallel Equivalent of General Relativity (TEGR) and Symmetric Teleparallel Equivalent of General Relativity (STEGR). We will show that the identification of gravity with spacetime curvature is not unique but a mere convention. These theories give two other equivalent but conceptually very different ways to look at gravity. We will show that classically all three theories are indistinguishable and which one represents the reality we do not know.

This paper describes theoretical work done in an attempt to find a physical mechanism for the gravitational and electric forces. This work demonstrates how both forces can be described as acoustic radiation forces (Bjerknes forces) which... more

This paper describes theoretical work done in an attempt to find a physical mechanism for the gravitational and electric forces. This work demonstrates how both forces can be described as acoustic radiation forces (Bjerknes forces) which exist in a vacuum with fluid properties. Vacuum parameters are derived for use in both Bjerknes force equations to demonstrate the equivalency of these equations to Newton’s gravitational force law and Coulomb’s law.

This book is a thought came to my mind recently about a question of what will happen if I changed my mathematical derivations? Will I come to the same result or something could be big deal and bigger than my present works? So I searched... more

This book is a thought came to my mind recently about a question of what will happen if I changed my mathematical derivations? Will I come to the same result or something could be big deal and bigger than my present works?
So I searched to certain point that I can change it without change or alter my idea or my procedures that I adopted. So I came up to these equations,
dU/dt=(c^3/4GM) ((〖 c〗^2 r)/2GM-1)^(1/2) e^(((〖 c〗^2 r)/2GM) ) sinh⁡((c^3 t)/4GM)
dV/dt=(c^3/4GM) ((〖 c〗^2 r)/2GM-1)^(1/2) e^(((〖 c〗^2 r)/2GM) ) cosh⁡((c^3 t)/4GM)
Which were the start point on my book 8th episode and former books. In these equations I did derivation respect to the time, then I asked, what about derivation respect to the radius instead of time? What will happen if I related anything to radius? I began on this book with these equations:
dU/dr=〖 c〗^4/(8G^2 M^2 ) ((〖 c〗^2 r)/2GM-1)^(-1/2) e^(((〖 c〗^2 r)/2GM) ) sinh⁡((c^3 t)/4GM)
dV/dr=〖 c〗^4/(8G^2 M^2 ) ((〖 c〗^2 r)/2GM-1)^(-1/2) e^(((〖 c〗^2 r)/2GM) ) cosh⁡((c^3 t)/4GM)
The results must carry most of Ali’s theory features like: De Sitter space, exponential energy patterns, strange momentum, symmetry breaking and emerging of dimensions and masses, and Ali’s law for space symmetry.
Until now I don’t know the usefulness of these different results but I will know because I followed my steps that I did for time but here I do for radius.
Maybe time is naturally changed so my previous results agreed with experiments, but here I deal with time flow rate which is inverse of time dilation, and here, first of all, I found that the high momentum in De Sitter equation resulted of the hugeness of time flow rate that breaks the law of light speed, and the mass exist to correct it. I think our universe’s vacuum and the huge empty space works entirely at the opposite of Einstein laws of relativity and one of the resultant of that is the exponential expansion later on. Thus I am sure in future there will be many explorations and discoveries that agreed with the results of this book.
#Ali_Yousif_Hassan_Edriss

We have studied primordial non-Gaussian features from a model of potential driven single field DBI Galileon inflation. We have computed the bispectrum from the three point correlation function considering all possible cross correlation... more

We have studied primordial non-Gaussian features from a model of potential driven single field DBI Galileon inflation. We have computed the bispectrum from the three point correlation function considering all possible cross correlation between scalar and tensor modes from the proposed setup. Further, we have computed the trispectrum from four point correlation function considering the contribution from contact interaction, scalar and graviton exchange diagrams in the in-in picture. Finally we have obtained the non-Gaussian consistency conditions from the four point correlator, which results in partial violation of the Suyama-Yamaguchi four-point consistency relation. This further leads to the conclusion that sufficient primordial non-Gaussianities can be obtained from DBI Galileon inflation.