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

TL;DR

This paper demonstrates that embedding theory naturally leads to Einstein's equations after inflation, suggesting it can serve as a fundamental framework for gravity without extra constraints, suitable for quantum gravity development.

Contribution

It shows that the embedding theory inherently removes extra solutions and converges to Einstein's equations post-inflation without additional modifications.

Findings

Einstein equations are satisfied with high precision after inflation.

Embedding theory can explain observed gravitational phenomena without extra constraints.

Potential for developing quantum gravity in a flat ambient space.

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.