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 with 95% confidence to be ${Omega}_{GW}(H_0/73 {rm km} {rm s}^{-1} {rm Mpc}^{-1})^2 < 1.3 times 10^{-9}$ at a frequency of 2.8 nHz, which is approximately a factor of six 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 simulations is inconsistent with our limit with 50% probability.
