  I investigate the impact of a "would be" fundamental symmetry of the laws of
nature under the interchange of gravity and antigravity, on the understanding
of negative energies in general relativity. For this purpose a toy model that
is based on Einstein-Hilbert gravity with two minimally coupled
self-interacting scalar fields is explored, where the second (exotic) scalar
field with negative energy density may be regarded, alternatively, as an
antigravitating field with positive energy. Spontaneous breakdown of reflection
symmetry is then considered in order to discuss the implications the proposed
"would be" fundamental symmetry might have for the vanishing of the
cosmological constant. A possible connection of the gravity-antigravity
symmetry with the so called quintom field is also explored.
