Architectures for a Space-based Gravitational-Wave Observatory

The European Space Agency (ESA) selected the science theme, the ``Gravitational Universe,'' for the third large mission opportunity, known as L3, under its Cosmic Vision Programme. The planned launch date is 2034.~ ESA is considering a 20{\%} participation by an international partner, and NASA's Astrophysics Division has begun negotiating a NASA role. We have studied the design consequences of a NASA contribution, evaluated the science benefits and identified the technology requirements for hardware that could be delivered by NASA. The European community proposed a strawman mission concept, called eLISA, having two measurement arms, derived from the well studied LISA (Laser Interferometer Space Antenna) concept.~ The US community is promoting a mission concept known as SGO Mid (Space-based Gravitational-wave Observatory Mid-sized), a three arm LISA-like concept. If NASA were to partner with ESA, the eLISA concept could be transformed to SGO Mid by the addition of a third arm, thereby augmenting science, reducing risk and reducing non-recurring engineering costs. The characteristics of the mission concepts and the relative science performance of eLISA, SGO Mid and LISA are described.