From the Embedding Theory to General Relativity in a result of inflation

Abstract

We study the embedding theory being a formulation of the gravitation theory where the independent variable is the embedding function for the four-dimensional space-time in a flat ambient space. We do not impose additional constraints which are usually used to remove from the theory the extra solutions not being the solutions of Einstein equations. In order to show the possibility of automatic removal of these extra solutions we analyze the equations of the theory, assuming an inflation period during the expansion of the Universe. In the framework of FRW symmetry we study the initial conditions for the inflation, and we show that after its termination the Einstein equations begin to satisfy with a very high precision. The properties of the theory equations allow us to suppose with confidence that the Einstein equations will satisfy with enough precision out of the framework of FRW symmetry as well. Thus the embedding theory can be considered as a theory of gravity which explains observed facts without any additional modification of it and we can use this theory in a flat space when we try to develop a quantum theory of gravity.

LaTeX, 18 pages; in this version some references was added

References in corpus (2)

• Ostrogradski approach for the Regge-Teitelboim type cosmology
• Dirac Relaxation of the Israel Junction Conditions: Unified Randall-Sundrum Brane Theory

Cited by in corpus (28)

• Embedding theory as new geometrical mimetic gravity
• Non-relativistic limit of embedding gravity as General Relativity with dark matter
• Hawking into Unruh mapping for embeddings of hyperbolic type
• Modifications of gravity via differential transformations of field variables
• Dark matter from non-relativistic embedding gravity
• Global Embedding of the Reissner-Nordström Metric in the Flat Ambient Space
• Hamilton-Jacobi approach for Regge-Teitelboim cosmology
• External time canonical formalism for gravity in terms of embedding theory
• Global embeddings of BTZ and Schwarzschild-AdS type black holes in a flat space
• Classification of global minimal embeddings for nonrotating black holes
• Dark matter as a gravitational effect in the embedding theory approach
• Algebra of Implicitly Defined Constraints for Gravity as the General Form of Embedding Theory
• Weak field limit for embedding gravity
• Gravitational energy in the framework of embedding and splitting theories
• Analytical analysis of the origin of core-cusp matter density distributions in galaxies
• Friedmann cosmology in Regge-Teitelboim gravity
• Energy-momentum pseudotensor and superpotential for generally covariant theories of gravity of general form
• First order minisuperspace model for the Faddeev formulation of gravity
• Canonical formulation of embedding gravity in a form of General Relativity with dark matter
• GEMS embeddings of Schwarzschild and RN black holes in Painlevé-Gullstrand spacetimes
• Hamilton-Jacobi approach for linearly acceleration-dependent Lagrangians
• Canonical description for formulation of embedding gravity as a field theory in a flat spacetime
• Possible types of dark matter condensation in embedding gravity
• Relation between quantum effects in General Relativity and embedding theory
• Analysis of the equations of motion of fictitious matter in embedding theory
• Polyakov-like approach to the modified gravity and other geometric theories
• GEMS embeddings of Hayward regular black holes in massless and massive gravities
• Gravity as embedding theory and the distribution of matter in galaxies