  A search for Higgs boson pair production via vector-boson fusion is performed
in the Lorentz-boosted regime, where a Higgs boson candidate is reconstructed
as a single large-radius jet, using 140 fb$^{-1}$ of proton-proton collision
data at $\sqrt{s} = 13$ TeV recorded by the ATLAS detector at the Large Hadron
Collider. Only Higgs boson decays into bottom quark pairs are considered. The
search is particularly sensitive to the quartic coupling between two vector
bosons and two Higgs bosons relative to its Standard Model prediction,
$\kappa_{2V}$. This study constrains $\kappa_{2V}$ to $0.55 < \kappa_{2V} <
1.49$ at 95% confidence level. The value $\kappa_{2V} = 0$ is excluded with a
significance of 3.8 standard deviations with other Higgs boson couplings fixed
to their Standard Model values. A search for new heavy spin-0 resonances that
would mediate Higgs boson pair production via vector-boson fusion is carried
out in the mass range of 1-5 TeV for the first time under several model and
decay-width assumptions. No significant deviation from the Standard Model
hypothesis is observed and exclusion limits at 95% confidence level are
derived.
