Towards precise and accurate Cepheid chemical abundances for 1$\%$
  $\mbox{H}_0$ measurement: temperature determination
  One of the outstanding problems in modern physics is the origin is of
accelerated expansion of the universe. High-precision determinations of the
Hubble parameter $\mbox{H}_0$ at different redshifts provide direct insight
into the Universe expansion: equation of state of the Dark Energy, geometry and
curvature of space, sum of neutrino masses and isotropy of the Universe. We
investigate the effect of chemical composition on the classical distance ladder
based on Cepheids stars and Supernovae type Ia. Cepheids belonging to
Magellanic Clouds represent a natural anchor for the ladder, due to their
proximity and the very well known geometric distance. Accordingly, the LACES
collaboration collected the largest spectroscopic sample of MCs Cepheids,
containing more than 300 stars and more than 1200 medium-high resolution
spectra. Abundance measurements, performed by equivalent width and curve of
growth analysis, have been tested on a wide grid of synthetic spectra to
quantify the systematic arising from this procedure. We focus on the errors
arising from temperature measurements, using the Line Depth Ratio method. We
find that in order to not bias the final results many aspects (e.g. degeneracy
of the atmospheric parameters, instrumental set up etc.) should be explicitly
taken into account. In particular, there is a not negligible metallicity
dependence.
