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 _ { 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 \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 ) \ll 1 and G \mu / c ^ { 2 } < 5 \times 10 ^ { -11 } / \alpha for \alpha c ^ { 2 } / ( \Gamma G \mu ) \gg 1 .