# Gravitation and inertia; a rearrangement of vacuum in gravity 

Byurakan Astrophysical Observatory, Byurakan, 378433, Aragatsotn District, Armenia. E-mail: gago 50@yahoo.com 

G.Ter-Kazarian 

We address the gravitation and inertia in the framework of general gauge principle (GGP) which accounts for gravitation gauge group G R generated by hidden local internal symmetry implemented on the flat space. Following the method of phenomenological Lagrangians, we connect the group G R to nonlinear realization of the Lie group of distortion G D of local internal properties of six- dimensional flat space M 6 , which is assumed as a toy model underlying four-dimensional Minkowski space. We study geometrical structure of the space of parameters and derive the Maurer-Cartan’s structure equations. We treat distortion fields as Goldstone fields, to which the metric and connec- tion are related, and infer the group invariants and calculate conserved currents. The agreement between proposed gravitational theory and available observational verifications is satisfactory. Un- like the GR, this theory is free of fictitious forces, which prompts us to address separately the inertia from a novel view point. We construct relativistic field theory of inertia, which treats inertia as dis- tortion of local internal properties of flat space M 2 conducted under the distortion inertial fields . We derive the relativistic law of inertia (RLI) and calculate inertial force acting on the photon in gravitating system. In spite of totally different and independent physical sources of gravitation and inertia, the RLI furnishes justification for introduction of the Principle of Equivalence. Particular attention is given to realization of the group G R by the hidden local internal symmetry of abelian group U loc = U (1) Y × diag [ SU (2)] implemented on the space M 6 . This group has two generators, third component T 3 of isospin and hypercharge Y implying Q d = T 3 + Y/ 2 , where Q d is the dis- tortion charge operator assigning the number -1 to particles, but +1 to anti-particles. This entails two neutral gauge bosons that coupled to T 3 and Y . We address the rearrangement of vacuum state in gravity resulting from these ideas. The neutral complex Higgs scalar breaks the vacuum symmetry leaving the gravitation subgroup intact. The resulting massive distortion field component may cause an additional change of properties of spacetime continuum at huge energies above the threshold value. 

Keywords: Modified theories of gravity, Spontaneous breaking of symmetries, Field theory of inertia, Prin- ciple of Equivalence, A rearrangement of vacuum 

More than four centuries passed since the famous far- reaching discovery of Galileo (in 1602 − 1604) that all bodies fall at the same rate [1], which led to an early em- pirical version of suggestion that gravitation and inertia may somehow result from a single mechanism. Besides describing these early gravitational experiments, Newton in Principia Mathematica [2] has proposed a comprehen- sive approach to studying the relation between the gravi- tational and inertial masses of a body. Ever since there is an ongoing quest to understand the reason for the equal- ity of gravitational and inertial forces, which remains an intractable mystery. From its historical development this can be regarded as furnishing immediate support for the Principle of Equivalence asserted by Einstein for General Relativity (GR), which preserves the idea of relativity of all kinds of motion. Currently, the Earth-Moon-Sun sys- tem provides the best solar system arena for testing the Principle of Equivalence, for a review see e.g. [3, 4]. Any theory of gravitation might explain both the attraction of masses and inertia in consistent terms. However, a nature of the relationship of gravity and inertia contin- ues to elude us and, beyond the Principle of Equivalence, there has been little progress in discovering their true re- lation. Moreover, it seemed that the inertia cannot be ultimately identified with the gravity as it is proposed 

## I. INTRODUCTION 

in GR, because there are important reasons to question the validity of this description. Actually, there are sev- eral empirical effects that seem incomprehensible in this framework. The experiments by [5–7] tested the impor- tant question of anisotropy of inertia stemming from the idea that the matter in our galaxy is not distributed isotropically with respect to the earth, and hence if the inertia is due to gravitational interactions then the in- ertial mass of a body will depend on the direction of its acceleration with respect to the direction towards the center of our galaxy. However, these experiments do not found such anisotropy of mass. For example, the most sensitive test is obtained in [7] from a nuclear magnetic resonance experiment, where the increase in sensitivity over that which one could obtain from M¨ o ssbaur effect is due to the far narrower line width obtainable for a tran- sition with a Li 7 nucleus of spin I = 3 / 2 in its ground state as compared with a nucleus in an excited state. If the mass anisotropy effect is present, there will be three different intervals which will lead to a triplet nuclear res- onance line, if the structure is resolved, or to a single broadened line if the structure is unresolved. The mag- netic field was of about 4700 gauss. The south direction in the horizontal plane points within 22 degrees towards the center of our galaxy, and 12 hour later this same di- rection along the earth’s horizontal plane points 104 de- grees away from the galactic center. If the nuclear struc- 

