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 (USM). This eliminates
the need to simulate the many thousands of network realisations 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 ~20-30 seconds on a
single CPU. Our formalism facilitates an efficient approach to computing Cosmic
Microwave Background (CMB) anisotropies for cosmic strings. Discretising the
UETC and performing an eigen-decomposition to act as sources in the CAMB CMB
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
realisations 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 ~30 hours on a modern single threaded CPU
for 2000 network realisations. Similar percent level accuracy can be achieved
with our approach on a moderately threaded CPU (8 threads) in only ~15 minutes.
If accuracy is only required at the 10 percent level and the CPU is more highly
threaded, cosmic string power spectra are now possible in ~2-3 minutes. This
makes exploration of the string parameter space now possible for
Markov-Chain-Monte-Carlo (MCMC) analysis.
