The cosmic microwave background (CMB) is affected by the total radiation density around the time of decoupling. At that epoch, neutrinos comprised a significant fraction of the radiative energy, but there could also be a contribution from primordial gravitational waves with frequencies greater than $\sim {10}^{-15}\mathrm{Hz}$. If this cosmological gravitational wave background were produced under adiabatic initial conditions, its effects on the CMB and matter power spectrum would mimic massless noninteracting neutrinos. However, with homogenous initial conditions—as one might expect from certain models of inflation, prebig bang models, phase transitions, and other scenarios—the effect on the CMB would be distinct. We present updated observational bounds for both initial conditions using the latest CMB data at small scales from the South Pole Telescope in combination with Wilkinson Microwave Anisotropy Probe, current measurements of the baryon acoustic oscillations, and the Hubble parameter. With the inclusion of the data from the South Pole Telescope, the adiabatic bound on the cosmological gravitational wave background density is improved by a factor of 1.7 to ${10}^6{\Omega }_{\mathrm{gw}}{h}^2\lesssim 8.7$ at the 95% confidence level, with weak evidence in favor of an additional radiation component consistent with previous analyses. The constraint can be converted into an upper-limit on the tension of horizon-sized cosmic strings that could generate this gravitational wave component, with $G\mu \lesssim 2\times {10}^{-7}$ at 95% C. L., for string tension $G\mu$. The homogeneous bound improves by a factor of 3.5 to ${10}^6{\Omega }_{\mathrm{gw}}{h}^2\lesssim 1.0$ at 95% C. L., with no evidence for such a component from current data.

• Received 30 March 2012

DOI:https://doi.org/10.1103/PhysRevD.85.123002