**Abstract** : Since the 2000s, many astrophysical observations have led to establishment of a standard model of cosmology, based on the existence of dark matter and dark energy to explain formation and the future of the Universe. Others theories like MOND (Modified Newtonian Dynamics) theory [1] or entropic gravity theory [2] give different explanations on universal gravitation theory either in order to explain galaxy rotation curve regardless existence of dark matter or to explain the origin of gravitational field and curvature of space-time by the mass. In the theory of relativity, the curvature of the space-time is imputed to the presence of mass or energy but no explanation is given to link presence of mass and curvature of the space-time. In other words, how, fundamentally, mass distorts space-time? How to explain, fundamentally, the equality between gravitational and inertial masses? This paper proposes to establish some theories to explain origin of inertia and by consequent, explain how mass distorts space-time and creates gravitational field. For that, this article proposes first to establish a relation linking the gravitational constant to the acceleration of the expansion of the Universe called. Moreover, this article proposes to model the evolution of the global Universe's "scale factor" without taking account of general relativity. That permits to explain nature of dark energy and unifies Hubble constant to gravitational constant as well as retrieving the literal value of the cosmological constant. Furthermore, explanation of origin of inertia needs to introduce a new form of gravitation field similar to magnetic field in the Maxwell electromagnetic theory and inspired by gravitoelectromagnetism theory. The new gravitational field, whose origin is linked to movement of mass, permits to retrieve some general relativity's results including polarization of gravitational waves predicted by Einstein as well as positions of photon sphere or innermost stable circular orbit in the case of non-rotary and electrically neutral central mass like a Schwarzschild black hole. It even permits to retrieve the general relativity's calculation of apsidal precession of an astronomical body's orbit in case of weak field approximation. Finally, this article proposes a model able to explain galaxy rotation curve as well as the evolution of their characteristic size related to the evolution of scale factor of the Universe and regardless existence of dark matter as unknown matter or regardless MOND theory. Index Terms-Gravitational constant, Acceleration of the expansion of the Universe, Energy density of the quantum vacuum, Cosmological constant, Dark mater, Dark energy, Hubble constant, Extraordinary gravitation field, Galaxy rotation curve I. GENERAL INTRODUCTION Two major discoveries have permitted to advance the cosmology science during the last 70 years without counting the advent of discoveries of Big Bang and the cosmic microwave background. The first one is the discovery of the non-ordinary mass distribution in galaxy M31 by Van de Hulst [3] and in galaxy M33 by Louise Volders [4]. The second one is the discovery of the acceleration of the expansion of the Universe by two independent projects in 1998 (the Supernova Cosmology Project and the High-Z Supernova Search Team) in measuring type Ia supernovae redshift and their apparent magnitude [5]. These two discoveries have led to consider that Universe is probably composed of dark matter and dark energy permitting respectively to explain formation of large-scale structure of the Universe and the current positive measurement of acceleration of the expansion of the Universe despite the fact that Universe is composed of around 10 80 massive particles [6], which should normally decelerate its expansion. However, nowadays, natures of dark matter and dark energy remain unknown and no dark matter particles as unknown particles have been yet detected even with advanced sensor technology [7]. Initial performance of the modern COSINE-100 experiment reproducing the DAMA/LIBRA experiment questions its conclusions about detection of annual modulation signal due to presence of dark matter particles [8]. Moreover, we can ask ourselves why Milky Way's dark matter halo which is supposed to be around 6.7 to 33 times more massive than radiant matter of the Milky Way [9][10] do not collapse to form dark matter black holes (even in form of a cloud) instead of having a spherical distribution? Even if that is not possible to form a compact object of dark matter, it could however be possible theoretically to collect enough dark matter particles in a volume included into a Schwarzschild radius to curb enough space-time to form massive black holes in the Universe. This affirmation is all the more relevant that dark matter does not interact electromagnetically and its compaction should be much easier than ordinary matter (baryon) for which, electromagnetic interactions impeach gravitational collapse. Indeed, for a given density of matter , Schwarzschild black hole radius is given by: * = √ 3 2 8 (0) With , the gravitational constant and , the celerity of light in the vacuum. Even if we do not exactly know global density of dark matter in the Universe, an estimated density of dark matter could be ~3 × 10 −29 g. −3 [11], which is potentially higher than critical density. That means dark matter cloud could form a black hole in our observable Universe of nearly radius of 8 billion light year, which is less than the radius of the observable Universe. Moreover, existence of this density of dark matter involves a curved shape of the Universe. Therefore, imposing existence of dark matter, as a cloud unable to collapse like ordinary matter, would lead to contradiction considering results from WMAP (Wilkinson Microwave Anisotropy Probe) revealing that Universe is flat with 0.4% margin of error [11]. Our article does not try to deny existence of dark matter but questions about its nature. It proposes a debate about potential nature of what dark matter could really be. This article proposes also to establish the probable nature of dark energy and highlights potential existence of a new gravitational field with different physical properties, compare to the classical known gravitational field's ones. Nima ZIAEI † Emerging gravitation in an accelerated expansion of the Universe-Probable natures of inertia, dark matter and dark energy † Physicist engineer at the ALTEN innovation center,