Space missions to detect the cosmic gravitational-wave background

It is thought that a stochastic background of gravitational waves was produced during the formation of the universe. A great deal could be learned by measuring this cosmic gravitational-wave background (CGB), but detecting the CGB presents a significant technological challenge. The signal strength is expected to be extremely weak, and there will be competition from unresolved astrophysical foregrounds such as white dwarf binaries. Our goal is to identify the most promising approach to detecting the CGB. We study the sensitivities that can be reached using both individual, and cross-correlated pairs of space-based interferometers. Our main result is a general, coordinate-free formalism for calculating the detector response that applies to arbitrary detector configurations. We use this general formalism to identify some promising designs for a gravitational background interferometer mission. Our conclusion is that detecting the CGB may not be out of reach.