Updated constraints on the cosmic string tension

We re-examine the constraints on the cosmic string tension from Cosmic Microwave Background (CMB) and matter power spectra, and also from limits on a stochastic background of gravitational waves provided by pulsar timing. We discuss the different approaches to modeling string evolution and radiation. In particular, we show that the unconnected segment model can describe CMB spectra expected from thin string (Nambu) and field theory (Abelian-Higgs) simulations using the computed values for the correlation length, rms string velocity and small-scale structure relevant to each variety of simulation. Applying the computed spectra in a fit to CMB and SDSS data we find that $G\mu/c^2< 2.6\times 10^{-7}$ ($2 \sigma$) if the Nambu simulations are correct and $G\mu /c^2< 6.4\times 10^{-7}$ in the Abelian-Higgs case. The degeneracy between $G\mu/c^2$ and the power spectrum slope $n_{\rm S}$ is substantially reduced from previous work. Inclusion of constraints on the baryon density from Big Bang Nucleosynthesis (BBN) imply that $n_{\rm S} <1$ at around the $4\sigma$ level for both the Nambu and Abelian-Higgs cases. As a by-product of our results, we find there is "moderate-to-strong" Bayesian evidence that the Harrison-Zel'dovich spectrum is excluded (odds ratio of $\sim 100:1$) by the combination of CMB, SDSS and BBN when compared to the standard 6 parameter fit. Using the contribution to the gravitational wave background from radiation era loops as a conservative lower bound on the signal for specific values of $G\mu/c^2$ and loop production size, $\alpha$, we find that $G\mu /c^2< 7\times 10^{-7}$ for $\alpha c^2/(\Gamma G\mu)\ll1$ and $G\mu/c^2 < 5\times 10^{-11}/\alpha$ for $\alpha c^2/(\Gamma G\mu) \gg1$.