Fast Analytic Computation of Cosmic String Power Spectra

TL;DR

This paper introduces an analytic method to compute cosmic string power spectra efficiently, significantly reducing computation time and enabling extensive parameter space exploration for cosmological analyses.

Contribution

The authors develop an analytic expression for the cosmic string UETC within the USM, eliminating the need for extensive network simulations and enabling rapid power spectrum calculations.

Findings

Computation time reduced from ~30 hours to ~15 minutes on a single CPU.

Achieves similar accuracy with fewer eigenmodes compared to traditional methods.

Enables MCMC analysis of cosmic string parameters within minutes.

Abstract

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.