Higher curvature counter terms cause the bounce in loop cosmology

Abstract. In the loop approach to the quantisation of gravity, one uses a Hilbert space which is too singular for some operators to be realised as derivatives. This is usually addressed by instead using finite difference operators at the Planck scale, a process known as “polymerisation”. In the symmetry reduced example of loop cosmology, we study an ambiguity in the regularisation which we relate to the ambiguity of fixing the coefficients of infinitely many higher curvature counter terms augmenting the Einstein-Hilbert action. Thus the situation is comparable to he one in a naive perturbative treatment of quantum gravity with a cut-off where the necessary presence of infinitely many higher derivative terms compromises predictability. As a by-product, we demonstrate in an appendix that it is possible to have higher curvature actions for gravity which still lead to first order equations of motion like in the Friedmann case. Preprint LMU-ASC 58/09 1