S. Capozziello et R. Deritis, NOTHER SYMMETRIES IN 4TH-ORDER COSMOLOGIES, Nuovo cimento della Societa italiana di fisica. B, Relativity, classical and statistical physics, 109(7), 1994, pp. 795-802
We apply the so-called Nother Symmetry Approach to a generic fourth-or
der theory of gravity f(R) to integrate the dynamics connected with th
e pointlike FRW cosmological Lagrangian. We get interesting results wh
en f(R) is-proportional-to R3/2, since in this case the equations of m
otion are exactly solvable and solutions are physically relevant.