  Parallaxes for 331 classical Cepheids, 31 Type II Cepheids and 364 RR Lyrae
stars in common between Gaia and the Hipparcos and Tycho-2 catalogues are
published in Gaia Data Release 1 (DR1) as part of the Tycho-Gaia Astrometric
Solution (TGAS). In order to test these first parallax measurements of the
primary standard candles of the cosmological distance ladder, that involve
astrometry collected by Gaia during the initial 14 months of science operation,
we compared them with literature estimates and derived new period-luminosity
($PL$), period-Wesenheit ($PW$) relations for classical and Type II Cepheids
and infrared $PL$, $PL$-metallicity ($PLZ$) and optical luminosity-metallicity
($M_V$-[Fe/H]) relations for the RR Lyrae stars, with zero points based on
TGAS. The new relations were computed using multi-band
($V,I,J,K_{\mathrm{s}},W_{1}$) photometry and spectroscopic metal abundances
available in the literature, and applying three alternative approaches: (i) by
linear least squares fitting the absolute magnitudes inferred from direct
transformation of the TGAS parallaxes, (ii) by adopting astrometric-based
luminosities, and (iii) using a Bayesian fitting approach. TGAS parallaxes
bring a significant added value to the previous Hipparcos estimates. The
relations presented in this paper represent first Gaia-calibrated relations and
form a "work-in-progress" milestone report in the wait for Gaia-only parallaxes
of which a first solution will become available with Gaia's Data Release 2
(DR2) in 2018.
