  Molecular line observations may serve as diagnostics of the degree to which
the number density of cosmic ray protons, having energies of 10s to 100s of
MeVs each, is enhanced in starburst galaxies and galaxies with active nuclei.
Results, obtained with the UCL\_PDR code, for the fractional abundances of
molecules as functions of the cosmic-ray induced ionisation rate, $\zeta$, are
presented. The aim is not to model any particular external galaxies. Rather, it
is to identify characteristics of the dependencies of molecular abundances on
$\zeta$, in part to enable the development of suitable observational programmes
for cosmic ray dominated regions (CRDRs) which will then stimulate detailed
modelling. For a number density of hydrogen nuclei of of $10^4$ cm$^{-3}$, and
high visual extinction, the fractional abundances of some species increase as
$\zeta$ increases to $10^{-14}$ s$^{-1}$, but for much higher values of $\zeta$
the fractional abundances of all molecular species are significantly below
their peak values. We show in particular that OH, H$_{2}$O, H$_{3}^{+}$,
H$_{3}$O$^{+}$ and OH$^{+}$ attain large fractional abundances ($\geqslant
10^{-8}$) for $\zeta$ as large as $10^{-12}$ s$^{-1}$. HCO$^{+}$ is a poor
tracer of CRDRs when $\zeta > 10^{-13}$ s$^{-1}$. Sulphur-bearing species may
be useful tracers of CRDRs gas in which $\zeta \sim 10^{-16}$ s$^{-1}$. Ammonia
has a large fractional abundance for $\zeta \leqslant 10^{-16}$ s$^{-1}$ and
nitrogen appears in CN-bearing species at significant levels as $\zeta$
increases, even up to $\sim 10^{-14}$ s$^{-1}$. In this paper, we also discuss
our model predictions, comparing them to recent detections in both galactic and
extragalactic sources. We show that they agree well, to a first approximation,
with the observational constraints.
