  Pulsar Timing Arrays have yet to convincingly observe gravitational waves.
Some time ago it was pointed out by one of the authors that a dramatic
enhancement of the signal would take place for particular values of the angle
subtended by the source and the observed pulsar. This enhancement is due to the
fact that waves propagate in a Friedmann-Lemaitre-Robertson-Walker metric
where, contrary to some wide-spread belief, a simple harmonic function with a
red-shifted frequency is not a solution of the equation of motion. At the first
non-trivial order, proper solutions have an effective wave number that differs
from the frequency. This leads to some interesting effects in Pulsar Timing
Arrays whose most visible manifestation is the enhancement of the signal that,
all other parameters kept fixed, is related in a simple manner to the value of
$H_0$. In this work, we rederive in an alternative way the main results, extend
the formalism to a more realistic setting where all components in the
cosmological budget are included, investigate in detail the dependence of the
signal on the various parameters involved and propose an observational set-up
to hopefully detect this very relevant effect.
