Upper limits on the cosmological gravitational wave background and maser clocks in space

We consider the possibility of detecting gravitational waves through the measurement of a time varying phase shift using a hydrogen maser clock on a satellite. Such measurements enable us to put interesting upper limits on the contribution of the gravitational-wave background to the dimensionless density of the Universe. The requirements on residual accelerations and the sensitivity of an accelerometer on the spacecraft are shown to be realistic and could be achieved using the accelerometer technology developed by ONERA for the ARISTOTELES mission. Such an experiment placing upper limits on the cosmological gravitational wave background could be conducted using the proposed Russian satellite Millimetron.On leave from the Astro Space Center, Lebedev Physical Institute, Moscow, Russia