  In order to understand the evolution and feedback of Active Galactic Nuclei
(AGN) and star formation it is important to use molecular lines as probes of
physical conditions and chemistry. We use H$_{2}$S to investigate the impact of
starburst and AGN activity on the chemistry of the molecular interstellar
medium in luminous infrared galaxies. Using the APEX single dish telescope, we
have observed the $1_{10}$--$1_{01}$ transition of ortho-H$_{2}$S at 168 GHz
towards the centres of twelve nearby luminous infrared galaxies. We have also
observed the same line towards the ultra luminous infrared galaxy (ULIRG)
Mrk~231 with the NOEMA interferometer. We have detected H$_{2}$S towards
NGC~253, NGC~1068, NGC~3256, NGC~4418, NGC~4826, NGC~4945, Circinus, M~83 and
Mrk~231. Four galaxies show elevated H$_{2}$S emission relative to HCN. We
suggest that the high line ratios are caused by elevated H$_{2}$S abundances in
the dense gas. However, we do not find any clear connection between the
H$_{2}$S/HCN line intensity ratio, and the presence (or speed) of molecular
outflows in the sample galaxies. Therefore H$_{2}$S abundances do not seem to
be globally affected by the large-scale outflows. We discuss possible
mechanisms behind the suggested H$_{2}$S abundance enhancements in NGC~4418,
Circinus, NGC~3256 and NGC~4826. These include radiative processes (for example
X-rays or cosmic-rays) or smaller scale shocks. We suggest that
$L_{\mathrm{H_{2}S}}$ serves as a tracer of the dense gas content, similar to
$L_{\mathrm{HCN}}$, and that the correlation between $L_{\mathrm{H_{2}S}}$ and
$M_{\rm outflow}$(H$_2$) implies a relation between the dense gas reservoir and
the properties and evolution of the molecular feedback. This potential link
requires further study since it holds important keys to our understanding of
how the properties of molecular outflows relate to that of their host galaxies.
