Cosmology and Statistics

Marginalized 68% and 95% confidence levels for ns, and r from Planck+WP and BAO data, compared to the theoretical predictions of selected inflationary models.

Credit: Planck Collaboration

Recent remarkable progress in cosmology is driven by vast observational data. Statistical analysis of these observational data constitutes an essential part of studies to explore physics behind the history and structure of the Universe. In particular, proper use of statistical quantities is a central issue of cosmology, because cosmological information is encoded in the fluctuations of the spatial distributions of astronomical objects. While the initial fluctuations are known to follow Gaussian statistics, fluctuations in the present Universe are quite non-Gaussian as a consequence of the evolution of the fluctuations via the gravitational instability, characterization of which requires the higher order statistics beyond the two-point correlation function. This is a highly mathematical problem and is also one of the main theme in the research program of the Cosmology and Statistics Group at the Kavli IPMU.

Another important problem in the comparison between theoretical models and observations is efficient parameter inference and model selection based on statistics. For example, Markov chain Monte Carlo methods and Bayesian statistics have been introduced to cosmological analysisrelatively recently, which significantly advanced analysis of cosmological data. New large-area surveys such as Subaru HSC/PFS will increase a tendency for applying sophisticated statistical techniques to the observational data. At the Kavli IPMU, cosmologists and mathematicians work together to tackle this problem and explore possible applications of new statistical techniques to cosmological analysis.

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