Fast analytic computation of cosmic string power spectra

We present analytic expressions for the cosmic string unequal time correlator (UETC) in the context of the Unconnected Segment Model. This eliminates the need to simulate the many thousands of network realizations needed to estimate the UETC numerically.With our approach we can compute the UETC very accurately, over all scales of interest, in the order of similar to 20-30 seconds on a single CPU. Our formalism facilitates an efficient approach to computing cosmic microwave background anisotropies for cosmic strings. Discretizing the UETC and performing an eigendecomposition to act as sources in the CAMB cosmic microwave background code, the power spectrum can be calculated by summing over a finite number of eigenmodes. A much smaller number of eigenmodes are required compared to the conventional approach of averaging power spectra over a finite number of realizations of the string network. With the additional efficiency and performance improvements offered by the OpenMP CAMB code, the time required to compute string power spectra is significantly reduced compared to the standard serial CMBACT code. The latter takes similar to 30 hours on a modern single threaded CPU for 2000 network realizations. Similar percent level accuracy can be achieved with our approach on a moderately threaded CPU (eight threads) in only similar to 15 minutes. If accuracy is only required at the 10% level and the CPU is more highly threaded, cosmic string power spectra are now possible in similar to 2-3 minutes. This makes exploration of the string parameter space now possible for Markov chain Monte Carlo analysis.