The usual “Copenhagen interpretation” emphasizes the role of a human experimenter, outside the system being discussed, making measurements, typically on multiple copies of the system. Such an interpretation is hardly suitable for describing the universe, and thus quantum cosmology would be excluded. It was, by the way, Hartle and Stephen Hawking who gave quantum cosmology an important boost with their paper “The Wave Function of the Universe.”
http://tuvalu.santafe.edu/~mgm/Site/Research.html
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http://www.nature.com/nature/journal/v443/n7108/full/443145a.html
http://www.nature.com/scientificamerican/journal/v242/n4/pdf/scientificamerican0480-118.html
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https://publications.lbl.gov/islandora/object/ir%3A90767