  Modified gravity theories are supposed to incorporate low-energy
quantum-gravity effects and, at the same time, they could shed light into the
dark matter and dark energy problems. Here we study a particular modification
of general relativity where local Lorentz invariance is spontaneously broken
and whose physical effects, despite a decade-long effort, were unknown. We show
that, during inflation, this modification produces anisotropies that would
generate measurable effects on the Cosmic Microwave Background. Then, by using
empirical constraints on the B-mode polarization spectrum, we can estimate that
the `coefficient' components absolute value have to be smaller than $10^{-43}$.
This is a remarkably strong limit, in fact, it is 29 orders of magnitude better
than the best constraints on similar coefficients. Thus, we propose that
inflation could stringently test other modified gravity theories.
