Cosmic gravitational-wave background: Limits from millisecond pulsar timing

We use seven years of millisecond pulsar-timing data to derive rigorous upper bounds on a cosmic gravitational-wave background. The energy density per logarithmic frequency interval near f=0.14 ${\mathrm{yr}}^{\mathrm{-}1}$ must be <9×${10}^{\mathrm{-}8}$ (68% confidence), or <4×${10}^{\mathrm{-}7}$ (95% confidence) of the density required to close the Universe. We detect a red-noise signal in the residuals for one pulsar. Its spectrum appears flatter than the ${\mathit{f}}^{\mathrm{-}5}$ power law expected for a gravity-wave background; likely noise sources include changes in the interstellar medium and pulsar rotational instabilities.