Avoidance of Singularity and Global Non-Conservation of Energy in General Relativity

TL;DR

This paper argues that singularities and energy non-conservation in General Relativity stem from its non-Machian, non-scale-invariant nature, proposing a scale-invariant theory and a negative energy component to address these issues and explain cosmic acceleration.

Contribution

It introduces a scale-invariant dynamical theory to avoid singularities and global energy non-conservation in General Relativity, and proposes a negative energy component for late-time cosmic acceleration.

Findings

Singularity in GTR is linked to non-Machian features.

A scale-invariant theory can avoid singularities.

A negative energy density component can drive late-time acceleration.

Abstract

We show that the singularity in the General Theory of Relativity (GTR) is the expression of a non-Machian feature. It can be avoided with a scale-invariant dynamical theory, a property lacking in GTR. It is further argued that the global non-conservation of energy in GTR also results from the lack of scale-invariance and the field formulation presented by several authors can only resolve the problem in part. Assuming the global energy conservation, we propose a negative energy density component with positive equation of state that can drive the late-time acceleration in the universe, while the positive component confines to smaller scales.