  There is a non-trivial four-derivative extension of the gravitational
spectrum that is free of ghosts and phenomenologically viable. It is the so
called $R^2$-gravity since it is defined by the only addition of a term
proportional to the square of the scalar curvature. Just the presence of this
term does not improve the ultraviolet behaviour of Einstein gravity but
introduces one additional scalar degree of freedom that can account for the
dark matter of our Universe.
