New life for the flat model of the universe in the post-Newtonian approximation of the theory of gravity

Abstract

A gravitational model of the flat (Euclidean geometry) universe in the post-Newtonian approximation of the theory of gravity (PNTG-approximation) was created. The PNTG- approximation provides the possibility of studying the internal gravitational field of bodies whose radius is equal to their gravitational radius . The flat universe belongs to such bodies. The generalized formula of Newton's gravitation (GFGN) was obtained, which allows studying the gravitational field inside a body with a radius . It was found that the field strength is zero at any point in the space-time of the Universe, reaches its maximum value at a distance from the selected point, and decreases again to zero at infinity (property of limited long-range gravity). This means that starting from the distance , the force of gravity from the side of the masses placed under the sphere with the radius decreases. Therefore, bodies (galaxies) at distances move faster than Hubble's law predicts. The property of limited long-range gravity is inherent in the static universe, so there is no reason to attribute the increased velocities of distant galaxies to "dark" energy. The theoretical estimate of the value of coincides with the conclusion established experimentally by astrophysicists that 5-6 billion years ago galaxies began to move at an accelerated rate, from our point of view - with increased speeds. The energetically zero model of the flat universe is substantiated. The disintegration of the vacuum into particles and antiparticles is accompanied by the formation of positive energy from the particles of material bodies, and negative energy of space from the antiparticles. The latter is realized in the process of expansion of the universe, in the forces opposing gravity - centrifugal, internal pressure and others. The formula for the complementarity of speeds is derived, according to which the square of the speed of movement of an event (body) along the spatial coordinate system in the sum of the square of the speed of its movement along the time axis is equal to the square of the speed of light . It was found that for a flat Universe, the speed of matter movement along the spatial axis and along the time axis are the same and equal to . The speed along the time axis is identified with the translational movement of galaxies, with the speed of their "aging", with the expansion of the universe. The speed along the spatial axis identified with mainly orbital movements of stars, planets, with the physical nature of internal pressure, with any energy that opposes gravity. According to the PNTG-model, it was found that the age of the flat universe is 20 billion years. The age of matter, taking into account that galaxies move at a speed of , is younger - 14.14 billion years. The increase in the speed of movement of galaxies occurred 5.98 billion years ago, experimentally established - 5-6 billion years ago. According to the Standard Model, the age of the universe is 13.8 billion years. The age of the substance is approximately the same 13.8 billion years. The age of stars and galaxies is less than 13.8 billion years. But if you take into account that the age of the universe is determined by the propagation of light, not matter, and, accordingly, is 19.5 billion years, then the Standard Model becomes identical to the PNTG model. This leads to the conclusion that the universe is actually flat and energetically neutral.