  We study modified theories of gravity of the f(R) type in Palatini formalism.
For a generic f(R) lagrangian, we show that the metric can be solved as the
product of a scalar function times a rank-two tensor (or auxiliary metric). The
scalar function is sensitive to the local energy-momentum density. The
auxiliary metric satisfies a set of equations very similar to Einstein's
equations and, for weak sources, it can be approximated by the Minkowski
metric. According to this, the metric coupled to the matter strongly departs
from the Minkowskian one in the neighbourhood of any microscopic physical
system. As a consequence, new gravitationally-induced interactions arise and
lead to observable effects at microscopic and macroscopic scales. In
particular, test body trajectories experience self-accelerations which depend
on the internal structure and composition of the body. These facts make very
unlikely the viability of Palatini f(R) models designed to change the late-time
cosmic evolution.
