Positive and Negative Energy Symmetry and the Cosmological Constant Problem

Abstract

The action for gravity and the standard model includes, as well as the positive energy fermion and boson fields, negative energy fields. The Hamiltonian for the action leads through a positive and negative energy symmetry of the vacuum to a cancellation of the zero-point vacuum energy and a vanishing cosmological constant in the presence of a gravitational field solving the cosmological constant problem. To guarantee the quasi-stability of the vacuum, we postulate a positive energy sector and a negative energy sector in the universe which are identical copies of the standard model. They interact only weakly through gravity. As in the case of antimatter, the negative energy matter is not found naturally on Earth or in the universe. A positive energy spectrum and a consistent unitary field theory for a pseudo-Hermitian Hamiltonian is obtained by demanding that the pseudo-Hamiltonian is ${\cal P}{\cal T}$ symmetric. The quadratic divergences in the two-point vacuum fluctuations and the self-energy of a scalar field are removed. The finite scalar field self-energy can avoid the Higgs hierarchy problem in the standard model.