A Machian Approach to Relativistic Cosmology

TL;DR

This paper develops a relativistic cosmological model grounded in Mach's principle, linking local inertial properties to the global mass-energy distribution, and aligns with General Relativity in local limits.

Contribution

It introduces a new geometric formulation of Mach's principle that integrates global mass-energy distribution with spacetime structure, extending relativistic cosmology.

Findings

The theory reduces to General Relativity locally.

Provides a criterion for Machian gravitational theories.

Analyzes cosmological implications of the Machian approach.

Abstract

We present a consistent relativistic formulation of Mach principle within a geometric theory of gravitation. In this approach, neither inertia nor free fall is assumed a priori. Instead, the motion of any local system arises from its dynamical interdependence, direct or indirect, with the rest of the Universe. This viewpoint provides a sharp criterion for what qualifies as a genuinely Machian gravitational theory. A theory is Machian only if the global mass energy distribution underwrites the very existence of the pseudo Riemannian structure of spacetime, rather than merely determining local features such as curvature on a pre existing background. We analyze the resulting cosmological model and discuss its phenomenological implications. In the appropriate local limit, the theory reduces to General Relativity, thereby preserving agreement with all Solar System tests.