We study semiconductor excitons confined in an electrostatic trap of a GaAs bilayer heterostructure. We evidence that optically bright excitonic states are strongly depleted while cooling to sub-Kelvin temperatures. In return, the other accessible an
d optically dark states become macroscopically occupied so that the overall exciton population in the trap is conserved. These combined behaviours constitute the spectroscopic signature for the mostly dark Bose-Einstein condensation of excitons, which in our experiments is restricted to a dilute regime within a narrow range of densities, below a critical temperature of about 1K.
