Global de Sitter space is unstable to particle creation, even for a massive free field theory with no self-interactions. The Bunch-Davies state is a definite phase coherent superposition of particle and anti-particle solutions in both the asymptotic past and future, and therefore is not a true vacuum state. In the closely related case of particle creation by a constant, uniform electric field, a time symmetric state analogous to the de Sitter invariant one is constructed, which is also not a stable vacuum state. The conformal anomaly plays a decisive role in the growth of perturbations and de Sitter symmetry breaking. Perturbations of the Bunch-Davies state contain additional massless scalar degrees of freedom arising from the anomaly not present in classical General Relativity. These conformal scalars can lead to substantial non-linear quantum backreaction effects in cosmology on horizon scales, variation of the dark energy of the universe in both space and time, and contribute to the observed Cosmic Microwave Background power spectrum and its potential non-gaussianities.