Compensational Gravity Fundamentals and an Application: The Cycling Universe

TL;DR

This paper introduces compensational gravity, an extension of Einstein's theory incorporating a compensation tensor to address quantum and anomaly issues, leading to a cyclic universe model explaining dark energy and dark matter.

Contribution

It proposes a novel extension of gravity theory with a compensation tensor, providing a unified framework for dark energy, dark matter, and cyclic cosmology.

Findings

Derivation of extended Einstein equations with a compensation tensor.

Natural emergence of cosmological constant, dark energy, and dark matter.

Construction of a cyclic universe model based on compensational gravity.

Abstract

Compensational gravity, which is regarded as a fundamental theory, is an advanced version of semiclassical gravity. It is a construction which extends the Einstein equation. Along with the energy-momentum tensor, the extended Einstein equation includes the compensation tensor, or compenson. The latter compensates for the energy-momentum tensor insufficiency, which consists in the discontinuity in time (due to quantum state reduction) and in space (due to sharp cutoff), as well as in an anomaly (nonrealistic state equation and nonzero divergence). The compenson is a primary object, for which equations are formulated. Specifically, purely dark objects may or may not exist. The dynamics of compensational gravity gives rise naturally to the cosmological constant, or dark energy and to dark matter: The compenson versus particle dark matter. On the basis of the dynamics, a cycling model of the closed universe is constructed.