  The notion of self-acceleration has been introduced as a convenient way to
theoretically distinguish cosmological models in which acceleration is due to
modified gravity from those in which it is due to the properties of matter or
fields. In this paper we review the concept of self-acceleration as given, for
example, by [1], and highlight two problems. First, that it applies only to
universal couplings, and second, that it is too narrow, i.e. it excludes models
in which the acceleration can be shown to be induced by a genuine modification
of gravity, for instance coupled dark energy with a universal coupling, the
Hu-Sawicki f(R) model or, in the context of inflation, the Starobinski model.
We then propose two new, more general, concepts in its place:
force-acceleration and field-acceleration, which are also applicable in
presence of non universal cosmologies. We illustrate their concrete application
with two examples, among the modified gravity classes which are still in
agreement with current data, i.e. f(R) models and coupled dark energy.
