The formation and growth processes of supermassive black holes (SMBHs) are not well constrained. SMBH population models, however, provide specific predictions for the properties of the gravitational-wave background (GWB) from binary SMBHs in merging galaxies throughout the universe. Using observations from the Parkes Pulsar Timing Array, we constrain the fractional GWB energy density (Ω(GW)) with 95% confidence to be Ω(GW)(H0/73 kilometers per second per megaparsec)(2) < 1.3 × 10(-9) (where H0 is the Hubble constant) at a frequency of 2.8 nanohertz, which is approximately a factor of 6 more stringent than previous limits. We compare our limit to models of the SMBH population and find inconsistencies at confidence levels between 46 and 91%. For example, the standard galaxy formation model implemented in the Millennium Simulation Project is inconsistent with our limit with 50% probability.

Gravitational waves are expected to be radiated by supermassive black hole binaries formed during galaxy mergers. A stochastic superposition of gravitational waves from all such binary systems would modulate the arrival times of pulses from radio pulsars. Using observations of millisecond pulsars obtained with the Parkes radio telescope, we constrained the characteristic amplitude of this background, A(c,yr), to be <1.0 × 10(-15) with 95% confidence. This limit excludes predicted ranges for A(c,yr) from current models with 91 to 99.7% probability. We conclude that binary evolution is either stalled or dramatically accelerated by galactic-center environments and that higher-cadence and shorter-wavelength observations would be more sensitive to gravitational waves.