Revisiting Cosmological parameter estimation

TL;DR

This paper demonstrates that particle swarm optimization (PSO) can effectively estimate cosmological parameters from CMB data, providing a complementary and efficient alternative to traditional Bayesian MCMC methods.

Contribution

The study shows PSO's capability to find best-fit parameters and sample parameter space effectively, matching MCMC results and offering advantages for blind searches in cosmology.

Findings

PSO yields consistent parameter estimates with MCMC methods.

PSO does not require covariance matrices or initial guesses.

Comparison of PSO with Nelder-Mead and BOBYQA methods.

Abstract

Constraining theoretical models with measuring the parameters of those from cosmic microwave background (CMB) anisotropy data is one of the most active areas in cosmology. WMAP, Planck and other recent experiments have shown that the six parameters standard $\Lambda$CDM cosmological model still best fits the data. Bayesian methods based on Markov-Chain Monte Carlo (MCMC) sampling have been playing leading role in parameter estimation from CMB data. In one of the recent studies \cite{2012PhRvD..85l3008P} we have shown that particle swarm optimization (PSO) which is a population based search procedure can also be effectively used to find the cosmological parameters which are best fit to the WMAP seven year data. In the present work we show that PSO not only can find the best-fit point, it can also sample the parameter space quite effectively, to the extent that we can use the same analysis pipeline to process PSO sampled points which is used to process the points sampled by Markov Chains, and get consistent results. We also present implementations of downhill-simplex Method of Nelder and Mead and Powell's method of Bound Optimization BY Quadratic Approximation (BOBYQA) in this work for cosmological parameter estimation, and compare these methods with PSO. Since PSO has the advantage that it only needs the search range and does not need covariance-matrix, starting point or any other quantity which depend on the final results, it can be quite useful for a blind search of the best fit parameters. Apart from that, PSO is based on a completely different algorithm so it can supplement MCMC methods. We use PSO to estimate parameters from the WMAP nine year and Planck data and get consistent results.