Causal boundary entropy from horizon conformal field theory

The effective quantum theory of near horizon regions of classical four-dimensional spatially Aat, Friedman-Robertson-Walker spacetimes is shown to be approximately a two-dimensional conformal field theory. The central charge and expectation value of the Hamiltonian of this theory, and the statistical entropy of horizon states which can be calculated using Cardy's formula, are all proportional to the horizon area in units of Newton's constant. The proportionality constant which is determined by Planck scare physics can be fixed such that the entropy is equal to a quarter of the horizon area in units of Newton's constant, in agreement with thermodynamic considerations.