  It is well a known fact that the Newtonian description of dynamics within
Galaxies for its known matter content is in disagreement with the observations
as the acceleration approaches $a_0 \approx 1.2 \times 10^{-10}m/s^2$ (slighter
larger for clusters). Both the Dark Matter scenario and Modified Gravity
Theories (MGT) fails to explain the existence of such an acceleration scale.
Motivated by the closeness of this acceleration scale and $c H_0\approx 10^{-9}
h$ $ m/s^2$, we analyse whether this coincidence might have a Cosmological
origin for scalar-tensor and spinor-tensor theories, performing detailed
calculations for perturbations that represent the local matter distribution on
the top of the cosmological background. Then, we solve the field equations for
these perturbations in a power series in the present value of the Hubble
constant. As we shall see, for both theories the power expansion contains only
even powers in the Hubble constant, a fact that renders the cosmological
expansion irrelevant for the local dynamics. At last, we show what a difference
a theory predicting linear terms in H makes in the local dynamics.
