We investigate the constraints that can be placed on the cosmic string tension by using the current pulsar timing array (PTA) limits on the gravitational wave background. We have developed a code to compute the spectrum of gravitational waves (GWs) based on the widely accepted one-scale model. In its simplest form the one-scale model for cosmic strings allows one to vary: (i) the string tension, $G\mu /c^2$; (ii) the size of cosmic string loops relative to the horizon at birth, $\alpha$; (iii) the spectral index of the emission spectrum, $q$; (iv) the cutoff in the emission spectrum, $n_{*}$; and (v) the intercommutation probability, $p$. The amplitude and slope of the spectrum in the nHz frequency range is very sensitive to these unknown parameters. We have also investigated the impact of more complicated scenarios with multiple initial loop sizes $\alpha$, in particular, the $2\mathrm{\text{−}}\alpha$ models proposed in the literature and a log-normal distribution for $\alpha$. We have computed the constraint on $G\mu /c^2$ due to the limit on a stochastic background of GWs imposed by the European Pulsar Timing Array. Taking into account all the possible uncertainties in the parameters we find a conservative upper limit of $G\mu /c^2<5.3\times {10}^{-7}$ which typically occurs when the loop production scale is close to the gravitational backreaction scale, $\alpha \approx \Gamma G\mu /c^2$. Stronger limits are possible for specific values of the parameters which typically correspond to the extremal cases $\alpha \ll \Gamma G\mu /c^2$ and $\alpha \gg \Gamma G\mu /c^2$. This limit is less stringent than the previously published limits which are based on cusp emission, an approach which does not necessarily model all the possible uncertainties. We discuss the prospects for lowering this limit by 2 orders of magnitude, or even a detection of the GW background, in the very near future in the context of the Large European Array for Pulsars and the Square Kilometre Array.

• Received 11 January 2012

DOI:https://doi.org/10.1103/PhysRevD.85.122003