Modified equations in the theory of induced gravity. Solution to the cosmological constant problem

TL;DR

This paper develops modified equations in induced gravity theory to address the cosmological constant problem, allowing for evolving gravitational and cosmological constants that can match observational data and differ from standard gravity.

Contribution

It introduces a self-consistent formulation of induced gravity with matter, enabling solutions with time-varying constants and phase transition-like behavior between Einstein and evolving gravity regimes.

Findings

Solutions can match standard gravity or differ from it.

Gravitational and cosmological constants evolve over time.

The theory describes phase transition-like behavior.

Abstract

This research is an extension of the author's article \cite{zar}, in which conformally invariant generalization of string theory was suggested to higher-dimensional objects. Special cases of the proposed theory are Einstein's theory of gravity and string theory. This work is devoted to the formation of self-consistent equations of the theory of induced gravity \cite{zar}, \cite{zari} in the presence of matter in the form of a perfect fluid that interacts with scalar fields. The study is done to solve these equations for the case of the cosmological model. In this model time-evolving gravitational and cosmological "constants" take place which are determined by the square of scalar fields. The values of which can be matched with the observational data. The equations that describe the theory have solutions that can both match with the solutions of the standard theory of gravity as well as it can differ from it. This is due to the fact that the fundamental "constants" of the theory, such as gravitational and cosmological, can evolve over time and also depend of the coordinates. Thus, in a rather general case the theory describes the two systems (stages): Einstein and "evolving" or "restructuring" (the name suggested by the author). This process is similar to the phenomenon of phase transition, where the different phases (Einstein gravity system, but with different constants) transit into each other.