  We develop a theory for fluctuations and correlations in a gas evolving under
ballistic annihilation dynamics. Starting from the hierarchy of equations
governing the evolution of microscopic densities in phase space, we
subsequently restrict to a regime of spatial homogeneity, and obtain explicit
predictions for the fluctuations and time correlation of the total number of
particles, total linear momentum and total kinetic energy. Cross-correlations
between these quantities are worked out as well. These predictions are
successfully tested against Molecular Dynamics and Monte-Carlo simulations.
This provides strong support for the theoretical approach developed, including
the hydrodynamic treatment of the spectrum of the linearized Boltzmann
operator. This article is a companion paper to arXiv:0801.2299 and makes use of
the spectral analysis reported there.
