  Banerji et al. (2009) suggested that top-heavy stellar Initial Mass Functions
(IMFs) in galaxies may arise when the interstellar physical conditions inhibit
low-mass star formation, and they determined the physical conditions under
which this suppression may or may not occur. In this work, we explore the
sensitivity of the chemistry of interstellar gas under a wide range of
conditions. We use these results to predict the relative velocity-integrated
antenna temperatures of the CO rotational spectrum for several models of high
redshift active galaxies which may produce both top-heavy and unbiased IMFs. We
find that while active galaxies with solar metallicity (and top-heavy IMFs)
produce higher antenna temperatures than those with sub-solar metallicity (and
unbiased IMFs) the actual rotational distribution is similar. The high-J to
peak CO ratio however may be used to roughly infer the metallicity of a galaxy
provided we know whether it is active or quiescent. The metallicity strongly
influences the shape of the IMF. High order CO transitions are also found to
provide a good diagnostic for high far-UV intensity and low metallicity
counterparts of Milky Way type systems both of which show some evidence for
having top-heavy IMFs. We also compute the relative abundances of molecules
known to be effective tracers of high density gas in these galaxy models. We
find that the molecules CO and CS may be used to distinguish between solar and
sub-solar metallicity in active galaxies at high redshift whereas HCN, HNC and
CN are found to be relatively insensitive to the IMF shape at the large visual
magnitudes typically associated with extragalactic sources.
