Fitting the Coupling Between Dark Energy and Dark Matter as Fields

Many parameterizations of couplings between dark energy (DE) and dark matter (DM) as fluids in the continuity equation have been studied in the literature, and observational data from the growth of perturbations can constrain these parameterizations. Instead, we present here a study of DE-DM coupling as fields, making use of the Boltzmann transport equation. This calculation required obtaining a distribution function for dark energy that leads to an equation of state parameter that is negative, which neither Bose-Einstein nor Fermi-Dirac statistics can supply. Treating dark energy as a quantum scalar field, we use adiabatic subtraction to obtain a finite analytic approximation for its distribution function that assumes the FLRW metric and nothing more. We present and examine our results for coupling via the graviton with no other explicit coupling in the Lagrangian. We then will fit the coupling parameter to supernovae and CMB data using COSMOMC.