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Emerging Gravitation in an Accelerated Expansion of the Universe – Probable Natures of Inertia, Dark Matter and Dark Energy

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Emerging Gravitation in an Accelerated Expansion of the Universe – Probable Natures of Inertia, Dark Matter and Dark Energy 1 Emerging gravitation in an accelerated expansion of the Universe – Probable natures of inertia, dark matter and dark energy Nima ZIAEI† † Physicist engineer at the ALTEN innovation center, Chaville, FRANCE Abstract— Since the 2000s, many astrophysical observations measuring type Ia supernovae redshift and their apparent have led to establishment of a standard model of cosmology, based magnitude [5]. These two discoveries have led to consider that on the existence of dark matter and dark energy to explain Universe is probably composed of dark matter and dark energy formation and the future of the Universe. Others theories like permitting respectively to explain formation of large-scale MOND (Modified Newtonian Dynamics) theory [1] or entropic structure of the Universe and the current positive measurement gravity theory [2] give different explanations on universal of acceleration of the expansion of the Universe despite the fact gravitation theory either in order to explain galaxy rotation curve 80 regardless existence of dark matter or to explain the origin of that Universe is composed of around 10 massive particles [6], gravitational field and curvature of space-time by the mass. In the which should normally decelerate its expansion. However, theory of relativity, the curvature of the space–time is imputed to nowadays, natures of dark matter and dark energy remain the presence of mass or energy but no explanation is given to link unknown and no dark matter particles as unknown particles presence of mass and curvature of the space-time. In other words, have been yet detected even with advanced sensor technology how, fundamentally, mass distorts space-time? How to explain, [7]. Initial performance of the modern COSINE-100 fundamentally, the equality between gravitational and inertial experiment reproducing the DAMA/LIBRA experiment masses? This paper proposes to establish some theories to explain questions its conclusions about detection of annual modulation origin of inertia and by consequent, explain how mass distorts space-time and creates gravitational field. For that, this article signal due to presence of dark matter particles [8]. Moreover, proposes first to establish a relation linking the gravitational we can ask ourselves why Milky Way’s dark matter halo which constant 푮 to the acceleration of the expansion of the Universe is supposed to be around 6.7 to 33 times more massive than called 횿. Moreover, this article proposes to model the evolution of radiant matter of the Milky Way [9][10] do not collapse to form the global Universe’s “scale factor” without taking account of dark matter black holes (even in form of a cloud) instead of general relativity. That permits to explain nature of dark energy having a spherical distribution? Even if that is not possible to and unifies Hubble constant 푯 to gravitational constant 푮 as well form a compact object of dark matter, it could however be as retrieving the literal value of the cosmological constant. possible theoretically to collect enough dark matter particles in Furthermore, explanation of origin of inertia needs to introduce a a volume included into a Schwarzschild radius to curb enough new form of gravitation field similar to magnetic field in the space-time to form massive black holes in the Universe. Maxwell electromagnetic theory and inspired by gravitoelectromagnetism theory. The new gravitational field, This affirmation is all the more relevant that dark matter does whose origin is linked to the movement of mass, permits to retrieve not interact electromagnetically and its compaction should be some general relativity’s results including polarization of much easier than ordinary matter (baryon) for which, gravitational waves predicted by Einstein as well as positions of electromagnetic interactions and electron degeneracy pressure photon sphere or innermost stable circular orbit in the case of non- impeach gravitational collapse. rotary and electrically neutral central mass like a Schwarzschild Indeed, for a given density of matter 휌, Schwarzschild black black hole. It even permits to retrieve the general relativity‘s hole radius is given by: calculation of apsidal precession of an astronomical body’s orbit in case of weak field approximation. Finally, this article proposes 3푐2 푅∗ = √ (0) a model able to explain galaxy rotation curve as well as the 푆퐵퐻 8휋퐺휌 evolution of their characteristic size related to the evolution of scale factor of the Universe and regardless existence of dark With 퐺, the gravitational constant and 푐, the celerity of light in matter as unknown matter or regardless MOND theory. the vacuum. Even if we do not exactly know global density of dark matter in the Universe, an estimated density of dark matter −29 −3 Index Terms— Gravitational constant, Acceleration of the could be 휌퐷푀~3 × 10 g. 푐푚 [11], which is potentially expansion of the Universe, Energy density of the quantum higher than critical density. That means dark matter cloud could vacuum, Cosmological constant, Dark mater, Dark energy, form a black hole in our observable Universe of nearly radius Hubble constant, Extraordinary gravitation field, Galaxy rotation of 8 billion light year, which is less than the radius of the curve observable Universe. Moreover, existence of this density of dark matter involves a curved shape of the Universe. Therefore, I. GENERAL INTRODUCTION imposing existence of dark matter, as a cloud unable to collapse Two major discoveries have permitted to advance the like ordinary matter, would lead to contradiction considering cosmology science during the last 70 years without counting the results from WMAP (Wilkinson Microwave Anisotropy Probe) advent of discoveries of Big Bang and the cosmic microwave revealing that Universe is flat with 0.4% margin of error [11]. background. The first one is the discovery of the non-ordinary Our article does not try to deny existence of dark matter but mass distribution in galaxy M31 by Van de Hulst [3] and in questions about its nature. It proposes a debate about potential galaxy M33 by Louise Volders [4]. The second one is the nature of what dark matter could really be. This article proposes discovery of the acceleration of the expansion of the Universe also to establish the probable nature of dark energy and by two independent projects in 1998 (the Supernova highlights potential existence of a new gravitational field with Cosmology Project and the High-Z Supernova Search Team) in 2 푠 different physical properties, compare to the classical known Considering now the work, done by metric constraint 퐹 , 퐴 푚 gravitational field’s ones. applied on the cubic parallelepiped (푐푝). As metric constraint is distributed on each of the six faces of the cubic parallelepiped, II. THE MASS AS INERTIA OF THE EXPANSION OF SPACE- 푠 the total work, done by metric constraint 퐹 , becomes: TIME 퐴 푚 6푠 푑푊 = 푑푊 (5 푏푖푠) A. Physical concept using weak field approximation 푐푝 퐴 Let be an electrically neutral and non-rotary spherical mass 푚 If we consider that, energy density of quantum vacuum is scale with a radius 푅0. An infinitesimal volume in spherical invariant [12] thereby; we can suppose a proportional coordinate, if we supposed to be in a Euclidian space, has for mathematical relation between 푑푊푐푝 and Δ(푑푉) as: 2 푠 expression 푑푉 = 4휋푟 푑푟. In a Schwarzschild metric, Because 푑푊 = 휎 × Δ(푑푉) (8) of the central mass 푚 this infinitesimal volume is expanded of 푐푝 퐴 푟=푅0 −3 value Δ(푑푉) as: With 휎 a homogenous parameter as energy density in J. 푚 Δ(푑푉) = Δ(4휋푟2) × 푑푟 + 4휋푟2 × Δ(푑푟) (1) that supposed to be the average energy density of quantum 2퐺푚 vacuum. Equation (8) stipulates that expansion of the slice of Considering 푚 as a weak mass ( ≪ 푅 ≤ 푟), expression of 푐2 0 space with a thickness 푑푟 due to presence of mass must Δ(푑푉) becomes: accumulate energy because of the non-variant scale factor of 8휋퐺푚푟 푟 vacuum energy density. Δ(푑푉) ≅ 2 (2 × ln ( ) + 1) × 푑푟 (2) 푐 푅0 Thus (2), (5 푏푖푠) and (8) involve: Generating expansion of the volume 푑푉 has consequence to 8휋휎퐺푚 퐹 (푅 ) = (9) accumulate energy into expanded volume Δ(푑푉) due to the 푚 0 3푐2 work of a supposed constraint applied on slice thickness 푑푟 of We can note that 퐹푚(푅0) is independent of 푅0. the space. In Newton gravitation theory of weak field, gravitational force is in 푟−2, so by a reaction mechanism, we B. The theory can consider that for 푟 = 푅0 constraint applied on the volume 푑푉 surrounding mass 푚 has for expression: Our theory is based on the idea that the matter as inertia, 휂 interacts with space-time in its accelerated expansion and ( ) 퐹(푟 = 푅0) = 2 3 caused by the global acceleration of the expansion of the 푅0 With 휂, a homogenous parameter that we are not trying to Universe. Without presence of mass, space-time normally accelerate its expansion but, in presence of any mass, express. Metric constraint for 푟 = 푅0 applied to the entanglement between matter and space-time impeaches constraint 퐹, noted 퐹푚, is given by the following expression: acceleration of expansion of space-time inside the matter. The 푑퐹 2퐹(푟 = 푅0) 퐹 (푅 ) = − | = (4) space-time remains “trapped” into matter and is curved outside 푚 0 푑푟 푅 푟=푅0 0 of it because of its accelerated expansion. Mathematically, our Let be a cubic parallelepiped at 푟 = 푅0 with an area per face 3 theory stipulates that it exists a direct relation between 퐹푚(푅0) 2 푠 ≪ 퐴 = 4휋푅0 with a total volume of 푠2. Considering the and Ψ representing global acceleration of the expansion of the −2 holographic principle [20], total physical information of any Universe (in 푠 ) as: ratio of the expanded volume Δ(푑푉) is encoded on the surface 퐹푚(푅0) = 푚 × Ψ (10) surrounding it.
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