Updated constraints on the cosmic string tension

We reexamine 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 x 10(-7) (2 sigma) if the Nambu simulations are correct and G mu/c(2) < 6.4 x 10(-7) in the Abelian-Higgs case. The degeneracy between G mu/c(2) and the power spectrum slope n(S) is substantially reduced from previous work. Inclusion of constraints on the baryon density from big bang nucleosynthesis (BBN) imply that n(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 similar to 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 x 10(-7) for alpha c(2)/(Gamma G mu) << 1 and G mu/c(2) < 5 x 10(-11)/alpha for alpha c(2)/(Gamma G mu) >> 1.