  The unexpected discovery of hot Jupiters challenged the classical theory of
planet formation inspired by our solar system. Until now, the origin and
evolution of hot Jupiters are still uncertain. Determining their age
distribution and temporal evolution can provide more clues into the mechanism
of their formation and subsequent evolution. Using a sample of 383 giant
planets around Sun-like stars collected from the kinematic catalogs of the
Planets Across Space and Time (PAST) project, we find that hot Jupiters are
preferentially hosted by relatively younger stars in the Galactic thin disk. We
subsequently find that the frequency of hot Jupiters declines with age. In
contrast, the frequency of warm/cold Jupiters shows no significant dependence
on age. Such a trend is expected from the tidal evolution of hot Jupiters'
orbits, and our result offers supporting evidence using a large sample. We also
perform a joint analysis on the planet frequencies in the stellar
age-metallicity plane. The result suggests that the frequencies of hot Jupiters
and warm/cold Jupiters, after removing the age dependence are both correlated
with stellar metallicities. Moreover, we show that the above correlations can
explain the bulk of the discrepancy in hot Jupiter frequencies inferred from
the transit and radial velocity (RV) surveys, given that RV targets tend to be
more metal-rich and younger than transits.
