  There is an ongoing debate on whether hot jupiter hosts are more likely to be
found in wide binaries with separations of $\gtrsim 100$ AU. In this paper, we
search for comoving, very wide companions with separations of $10^3-10^4$ AU
for hot jupiter hosts and main-sequence contact binaries in Gaia DR2, and
compare the very wide companion fractions with their object-by-object-matched
field star samples. We find that $11.9\pm 2.5$% of hot jupiter hosts and
$14.1\pm 1.0$% of contact binaries have companions at separations of
$10^3-10^4$ AU. While the very wide companion fraction of hot jupiter hosts is
a factor of $1.9\pm0.5$ larger than their matched field star sample, it is
consistent, within $\sim1\sigma$, with that of matched field stars if the
matching is only with field stars without close companions (within $\sim50$ AU)
as is the case for hot jupiter hosts. The very wide companion fraction of
contact binaries is a factor of $3.1\pm0.5$ larger than their matched field
star sample, suggesting that the formation and evolution of contact binaries
are either tied to or correlated with the presence of wide companions. In
contrast, the weak enhancement of very wide companion fraction for hot jupiter
hosts implies that the formation of hot jupiters is not as sensitive to those
environment properties. Our results also hint that the occurrence rates of dual
hot jupiter hosts and dual contact binaries may be higher than the expected
values from random pairing of field stars, which may be due to their underlying
metallicity and age dependence.
