K-matter as Mach's principle realization

TL;DR

This paper explores how Mach's principle, when integrated with quantum theory and Einstein's equations, leads to a universe model with K-matter, revealing connections to open de Sitter and Milne universes and discussing implications for cosmological data.

Contribution

It introduces a novel approach incorporating Mach's principle as a constraint, resulting in a new interpretation of matter and universe evolution within Einstein's framework.

Findings

Non-relativistic matter acts as K-matter under Mach's principle.

Exact solutions for universe models with K-matter and cosmological constant are derived.

The Machian universe with a cosmological constant resembles an open de Sitter universe.

Abstract

It is shown that if one takes into account Mach's principle in the form which follows from quantum theory and considers it as a complementary constraint between the parameters which characterize the energy density and geometry of the universe in addition to Einstein equations for a FRW universe, non-relativistic matter transforms into an analogue of K-matter. The exact solutions of the Einstein equations for the universe with such matter and cosmological constant are found. It is demonstrated that the Machian universe under consideration with a nonzero cosmological constant is equivalent to the open de Sitter universe. In the limit of zero cosmological constant such a universe evolves as a Milne universe, but in contrast to it, it contains matter with nonzero energy density. The possible application of proposed approach to the description of the present cosmological data is discussed. The problem of the age of the universe is considered as an example.