Mathematical problems in higher order gravity and cosmology

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We discuss the issue of motivating the analysis of higher order gravity theories and their cosmologies and introduce a rule which states that these theories may be considered as a vehicle for testing whether certain properties may be of relevance to quantum theory. We discuss the physicality issue arising as a consequence of the conformal transformation theorem, the question of formulating a consistent first order formalism of such theories and also the isotropization problem for a class of generalized cosmologies. We point out that this field may have an important role to play in clarifying issues arising also in general relativity.
3 pages, LaTeX, talk presented at the Eighth Marcel Grossmann Meeting, Jerousalem, June 22--27, 1997

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