Critical Cosmology in Higher Order Gravity
  We construct the higher order terms of curvatures in Lagrangians of the scale
factor for the Friedmann-Lemaitre-Robertson-Walker universe, which are linear
in the second derivative of the scale factor with respect to cosmic time. It is
shown that they are composed from the Lovelock tensors at the first step;
iterative construction yields arbitrarily high order terms. The relation to the
former work on higher order gravity is discussed. Despite the absence of scalar
degrees of freedom in cosmological models which come from our Lagrangian, it is
shown that an inflationary behavior of the scale factor can be found. The
application to the thick brane solutions is also studied.
