Cosmological Constant Implementing Mach Principle in General Relativity

TL;DR

This paper develops a conformal invariant extension of general relativity to incorporate Mach's principle at cosmological scales, resulting in field equations that avoid Einstein's issues with Mach's principle and align with Sciama's perspective.

Contribution

It introduces a conformal invariant model that extends GR to large scales and derives field equations consistent with Mach's principle without Einstein's traditional problems.

Findings

Derived cosmological field equations from a conformal invariant model.

The new equations are compatible with Mach's principle and avoid Einstein's de Sitter solution issues.

Provides a large-scale extension of GR consistent with operational definitions.

Abstract

We consider the fact that noticing on the operational meaning of the physical concepts played an impetus role in the appearance of general relativity (GR). Thus, we have paid more attention to the operational definition of the gravitational coupling constant in this theory as a dimensional constant which is gained through an experiment. However, as all available experiments just provide the value of this constant locally, this coupling constant can operationally be meaningful only in a local area. Regarding this point, to obtain an extension of GR for the large scale, we replace it by a conformal invariant model and then, reduce this model to a theory for the cosmological scale via breaking down the conformal symmetry through singling out a specific conformal frame which is characterized by the large scale characteristics of the universe. Finally, we come to the same field equations that historically were proposed by Einstein for the cosmological scale (GR plus the cosmological constant) as the result of his endeavor for making GR consistent with the Mach principle. However, we declare that the obtained field equations in this alternative approach do~not carry the problem of the field equations proposed by Einstein for being consistent with Mach's principle (i.e., the existence of de Sitter solution), and can also be considered compatible with this principle in the Sciama view.