Relativity and Cosmology


General Relativity and Dark Energy Are Hidden in the Klein-Gordon Equation in Curved Spacetime

Authors: Gary Nash

By maintaining the form of the Klein-Gordon equation in curved 4-dimensional spacetime, it can be symmetrized into symmetric and antisymmetric (2,0) tensors with the wave function $\Psi$ having spins $0,1,2,1/2$ and $3/2$. Using a decomposition of symmetric tensors and two fundamental principles of general relativity, a new tensor describing the energy-momentum of the gravitational field and dark energy appears naturally alongside the Einstein tensor. The tensors that constitute the modified Einstein equation add to zero. General relativity and dark energy are hidden in the symmetric part of the Klein-Gordon equation for each spin. As quantum field theory in curved spacetime is built from the free field solutions of the Klein-Gordon equation, general relativity and dark energy are hidden in the formalism of quantum field theory. The metric as a field variable describing gravitons vanishes from the massless spin-2 KG equation in the low-energy long-range to particle regimes of spacetime. Massless spin-2 gravitons in those regimes do not exist. Unlike the other three known fundamental forces in nature, no particle exchange is required to explain the force of gravity in those regimes. It is shown that the cosmological constant must be zero. Dark energy effectively replaces the cosmological constant and describes a cyclic universe which developed after the Big Bang. Dark energy is interpreted to be the repulsive part of the trace of the tensor describing the energy-momentum of the gravitational field and dark energy. The dark energy density provides a natural explanation of why the vacuum energy density is so small, and why it dominates the present epoch of the universe.

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[v1] 2017-09-18 09:35:00

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