  The decay rate of the Bunch-Davies state of a massive scalar field in the
expanding flat spatial sections of de Sitter space is determined by an analysis
of the particle pair creation process in real time. The Feynman definition of
particle and antiparticle Fourier mode solutions of the scalar wave equation,
and their adiabatic phase analytically continued to the complexified time
domain, show conclusively that the Bunch-Davies state is not the vacuum state
at late times. The closely analogous creation of charged particle pairs in a
uniform electric field is reviewed and Schwinger's result for the vacuum decay
rate is recovered by the real time analysis. The vacuum decay rate in each case
is also calculated by switching the background field on adiabatically, allowing
it to act for a very long time, and then adiabatically switching it off again.
In both the uniform electric field and de Sitter cases the particles created
while the field is switched on are verified to be real, in the sense that they
persist in the final asymptotic flat zero-field region. In the de Sitter case
there is an interesting residual dependence of the rate on how the de Sitter
phase is ended, indicating a greater sensitivity to spatial boundary
conditions. The electric current of the created particles in the E-field case
and their energy density and pressure in the de Sitter case are also computed,
and the magnitude of their backreaction effects on the background field
estimated. Possible consequences of the Hubble scale instability of the de
Sitter vacuum for cosmology, vacuum dark energy, and the cosmological
`constant' problem are discussed.
