Stability and Hamiltonian formulation of higher derivative theories

Abstract

We analyze the presumptions which lead to instabilities in theories of order higher than second. That type of fourth order gravity which leads to an inflationary (quasi de Sitter) period of cosmic evolution by inclusion of one curvature squared term (i.e. the Starobinsky model) is used as an example. The corresponding Hamiltonian formulation (which is necessary for deducing the Wheeler de Witt equation) is found both in the Ostrogradski approach and in another form. As an example, a closed form solution of the Wheeler de Witt equation for a spatially flat Friedmann model and L=R\sp 2 is found. The method proposed by Simon to bring fourth order gravity to second order can be (if suitably generalized) applied to bring sixth order gravity to second order. In the Erratum we show that a spatially flat Friedmann model need not be geodesically complete even if the scale factor a(t) is positive and smooth for all real values of the synchronized time t.