  The probability that a Sun-like star has a close-orbiting giant planet
(period < 1 year) increases with stellar metallicity. Previous work provided
evidence that the period distribution of close-orbiting giant planets is also
linked to metallicity, hinting that there two formation/evolution pathways for
such objects, one of which is more probable in high-metallicity environments.
Here, we check for differences in the period distribution of hot Jupiters (P <
10 days) as a function of host star metallicity, drawing on a sample of 232
transiting hot Jupiters and homogeneously-derived metallicities from Gaia Data
Release 3. We found no evidence for any metallicity dependence; the period
distributions of hot Jupiters around metal-poor and metal-rich stars are
indistinguishable. As a byproduct of this study, we provide transformations
between metallicities from the Gaia Radial Velocity Spectrograph and from
traditional high-resolution optical spectroscopy of main-sequence FGK stars.
