Torsion in loop space homology of rationally contractible spaces

Let R be a torsion free principal ideal domain. We study the growth of torsion in loop space homology of simply-connected DGR-coalgebras C, whose homology admits an exponent r in R. Hew by loop space homology we mean the homology of the loop algebra construction on C. We compute a bound on the growth of torsion in such objects and show that in general this bound is best possible. Our methods are applied to certain simply-connected spaces associated with classifying spaces of finite groups, where we are able to deduce the existence of global exponents in loop space homology.