Challenges in the Comparison of Theory and Observation in Cosmology: Recent Developments and Open Problems"
The standard theoretical scenario of large-scale structure formation begins with random initial density perturbations that subsequently undergo nonlinear gravitational collapse to form the observed "cosmic web". Both current and future experiments probe spatial scales of the Universe where the dynamics are nonlinear, making it challenging to extract information about the details of cosmological models from these observations. Unlike the analysis of the Cosmic Microwave Background, a computationally feasible implementation of an exact Bayesian approach to the inference of cosmological parameters from these measurements has not yet been fully developed.
Traditionally, this shortcoming has been overcome with the construction of approximate likelihood functions, quantifying the "goodness of fit" of cosmological model parameters to observations through agreement of various chosen "test statistics" (such as power spectra). Alternatively, progress continues to be made towards the implementation of a direct Bayesian approach, in which the history of our observable universe is inferred jointly with cosmological parameters.
I will review both paths to the comparison of theory and observation, inherent difficulties with both, recent progress, and open problems.