  In the framework of alternative metric gravity theories, it has been shown by
several authors that a generic Lagrangian depending on the Riemann tensor
describes a theory with 8 degrees of freedom (which reduce to 3 for f(R)
Lagrangians depending only on the curvature scalar). This result is often
related to a reformulation of the fourth-order equations for the metric into a
set of second-order equations for a multiplet of fields, including a massive
scalar field and a massive spin-2 field. In this article we investigate an
issue which does not seem to have been addressed so far: in ordinary
general-relativistic field theories, all fundamental fields (i.e. fields with
definite spin and mass) reduce to test fields in some appropriate limit of the
model, where they cease to act as sources for the metric curvature. In this
limit, each of the fundamental fields can be excited from its ground state
independently from the others. The question is: does higher-derivative gravity
admit a test-field limit for its fundamental fields? It is easy to show that
for a f(R) theory the test-field limit does exist; then, we consider the case
of Lagrangians quadratically depending on the full Ricci tensor. We show that
the constraint binding together the scalar field and the massive spin-2 field
does not disappear in the limit where they should be expected to act as test
fields, except for a particular choice of the Lagrangian, which cause the
scalar field to disappear (reducing to 7 DOF). We finally consider the addition
of an arbitrary function of the quadratic invariant of the Weyl tensor and show
that the resulting model still lacks a proper test-field limit. We argue that
the lack of a test-field limit for the fundamental fields may constitute a
serious drawback of the full 8 DOF higher-order gravity models, which is not
encountered in the restricted 7 DOF or 3 DOF cases.

General Relativity and Quantum Cosmology