  A search is presented for the resonant production of a pair of standard
model-like Higgs bosons using data from proton-proton collisions at a
centre-of-mass energy of 13 TeV, collected by the CMS experiment at the CERN
LHC in 2016-2018, corresponding to an integrated luminosity of 138 fb$^{-1}$.
The final state consists of two b quark-antiquark pairs. The search is
conducted in the region of phase space where at least one of the pairs is
highly Lorentz-boosted and is reconstructed as a single large-area jet. The
other pair may be either similarly merged or resolved, the latter reconstructed
using two b-tagged jets. The data are found to be consistent with standard
model processes and are interpreted as 95% confidence level upper limits on the
product of the cross sections and the branching fractions of the spin-0 radion
and the spin-2 bulk graviton that arise in warped extradimensional models. The
limits set are in the range 9.74-0.29 fb and 4.94-0.19 fb for a narrow radion
and a graviton, respectively, with masses between 1 and 3 TeV. For a radion and
for a bulk graviton with widths 10% of their masses, the limits are in the
range 12.5-0.35 fb and 8.23-0.23 fb, respectively, for the same masses. These
limits result in the exclusion of a narrow-width graviton with a mass below 1.2
TeV, and of narrow and 10%-width radions with masses below 2.6, and 2.9 TeV,
respectively.
