  Binary statistics of the latest-type T and Y brown dwarfs are sparse and it
is unclear whether the trends seen in the multiplicity properties of their more
massive counterparts hold for the very coolest brown dwarfs. We present results
from a search for substellar and planetary-mass companions to a sample of 12
ultracool T8$-$Y0 field brown dwarfs with the Hubble Space Telescope/Wide Field
Camera 3. We find no evidence for resolved binary companions among our sample
down to separations of 0.7$-$2.5 AU. Combining our survey with prior searches,
we place some of the first statistically robust constraints to date on the
multiplicity properties of the coolest, lowest-mass brown dwarfs in the field.
Accounting for observational biases and incompleteness, we derive a binary
frequency of $f = 5.5^{+5.2}_{-3.3}$% for T5$-$Y0 brown dwarfs at separations
of 1.5$-$1000 AU, for an overall binary fraction of $f_\mathrm{tot} = 8\pm6$%.
Modelling the projected separation as a lognormal distribution, we find a peak
in separation at $\rho_0 = 2.9^{+0.8}_{-1.4}$ AU with a logarithmic width of
$\sigma = 0.21^{+0.14}_{-0.08}$. We infer a mass ratio distribution peaking
strongly towards unity, with a power law index of $\gamma = 6.1^{+4.0}_{-2.7}$,
reinforcing the significance of the detection of a tighter and higher mass
ratio companion population around lower-mass primaries. These results are
consistent with prior studies and support the idea of a decreasing binary
frequency with spectral type in the Galactic field.
