In addition to the two standard solutions of the quantum field equations
having the form e^{+/-(iwt-ikx)}, there exist two additional solutions of the
form e^{+/-(iwt+ikx). By incorporating these latter solutions, deemed
"supplemental solutions", into the development of quantum field theory, one finds a
simple and natural cancellation of terms that results in an energy VEV, and a
cosmological constant, of zero. This fundamental, and previously unrecognized,
inherent symmetry in quantum field theory shows promise for providing a
resolution of the large vacuum energy problem, simply and directly, with little
modification or extension to the extant mathematics of the theory. In certain
scenarios, slight asymmetries could give rise to dark energy.
We study a symmetry, schematically Energy -> - Energy, which suppresses
matter contributions to the cosmological constant. The requisite negative energy
fluctuations are identified with a "ghost" copy of the Standard Model.
Gravity explicitly, but weakly, violates the symmetry, and naturalness requires
General Relativity to break down at short distances with testable consequences.
If this breakdown is accompanied by gravitational Lorentz-violation, the
decay of flat spacetime by ghost production is acceptably slow. We show that
inflation works in our scenario and can lead to the initial conditions required
for standard Big Bang cosmology.
We propose a method of field quantization which uses an indefinite metric in
a Hilbert space of state vectors. 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 charge
conjugation invariance 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. To guarantee the stability of the vacuum, we introduce a Dirac
sea `hole' theory of quantization for gravity as well as the standard model.
The vacuum is defined to be fully occupied by negative energy particles with
a hole in the Dirac sea, corresponding to an anti-particle. We postulate
that the negative energy bosons in the vacuum satisfy a para-statistics that
leads to a para-Pauli exclusion principle for the negative energy bosons in the
vacuum, while the positive energy bosons in the Hilbert space obey the usual
Bose-Einstein statistics. This assures that the vacuum is stable for both
fermions and bosons. Restrictions on the para-operator Hamiltonian density lead
to selection rules that prohibit positive energy para-bosons from being
observable. The problem of deriving a positive energy spectrum and a consistent
unitary field theory from a pseudo-Hermitian Hamiltonian is investigated.
I discuss possible implications a symmetry relating gravity with
antigravity might have for smoothing out of the cosmological constant puzzle. For this
purpose, a very simple model with spontaneous symmetry breaking is explored,
that is based on Einstein-Hilbert gravity with two self-interacting scalar
fields. The second (exotic) scalar particle with negative energy density, could
be interpreted, alternatively, as an antigravitating particle with positive
energy.
We outline the evaluation of the cosmological constant in the framework of
the standard field-theoretical treatment of vacuum energy and discuss the
relation between the vacuum energy problem and the gauge-group spontaneous
symmetry breaking. We suggest possible extensions of the 't Hooft-Nobbenhuis
symmetry, in particular, its complexification till duality symmetry and discuss the
compatible implementation on gravity. We propose to use the discrete
time-reflection transform to formulate a framework in which one can eliminate the
huge contributions of vacuum energy into the effective cosmological constant
and suggest that the breaking of time--reflection symmetry could be responsible
for a small observable value of this constant