Field Equations and Conservation Laws Derived from the Generalized Einstein Lagrangian Density for A Gravitational System and Their Implications to Cosmology

TL;DR

This paper derives modified Einstein field equations and conservation laws from a generalized Lagrangian, exploring their implications for cosmology and predicting new testable properties of the universe.

Contribution

It introduces a generalized Einstein Lagrangian density and systematically derives new field equations and conservation laws with potential cosmological implications.

Findings

New properties of the cosmos deduced

Predictions of effects testable by future experiments

Modified Einstein equations derived from generalized Lagrangian

Abstract

Based on investigations of the fundamental properties of the generalized Einstein Lagrangian density for a gravitational system, the theoretical foundations of the modified Einstein field equations and the Lorentz and Levi-Civita conservation laws are systematically studied. The theory of cosmology developed on the basis of these equations and laws is analyzed in detail. Some new properties and new effects of the cosmos are deduced; these new properties and new effects could be tested via future experiments and observations.