The properties of a planetary system may be influenced by properties of the host star, such as its birth environment or age. Recently, a link has been found between a star's local phase space density in the Galaxy and the presence of a hot Jupiter: hot Jupiters are preferentially found around stars with higher local phase space densities. Using kinematic data for exoplanet hosts from Gaia EDR3, we show that the phase space density is primarily determined by a star's Galactic kinematics -- notably, its orbital velocity around the Galactic centre relative to a circular orbit. Stars on kinematically "colder" orbits have higher local phase space densities than stars on kinematically "hotter" orbits. Once this effect is accounted for, we find no evidence that hot Jupiter hosts are in higher-density regions of phase space than other stars. Younger stars are on average on colder orbits, and older stars are on average on hotter orbits, so we argue that the preference for hot Jupiter hosts to be in high-density regions reflects an age bias: hot Jupiters are more common around younger stars, before their population is reduced by tidal inspiral. Our work gives a hint of the relations that PLATO may uncover when it provides precise and accurate ages for a large number of main-sequence exoplanet hosts.

AJM acknowledges funding from the Swedish Research Council (grant 2017-04945), the Swedish National Space Agency (grant 120/19C), and the Fund of the Walter Gyllenberg Foundation of the Royal Physiographic Society in Lund.

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