  A search for pairs of Higgs bosons produced via gluon and vector boson fusion
is presented, focusing on the four b quark final state. The data sample
consists of proton-proton collisions at a center-of-mass energy of 13 TeV,
collected with the CMS detector at the LHC, and corresponds to an integrated
luminosity of 138 fb$^{-1}$. No deviation from the background-only hypothesis
is observed. A 95% confidence level upper limit on the Higgs boson pair
production cross section is observed at 3.9 times the standard model prediction
for an expected value of 7.8. Constraints are also set on the modifiers of the
Higgs field self-coupling, $\kappa_\lambda$, and of the coupling of two Higgs
bosons to two vector bosons, $\kappa_\mathrm{2V}$. The observed (expected)
allowed intervals at the 95% confidence level are $-$2.3 $\lt$ $\kappa_\lambda$
$\lt$ 9.4 ($-$5.0 $\lt$ $\kappa_\lambda$ $\lt$ 12.0) and $-$0.1 $\lt$
$\kappa_\mathrm{2V}$ $\lt$ 2.2 ($-$0.4 $\lt$ $\kappa_\mathrm{2V}$ $\lt$ 2.5).
These are the most stringent observed constraints to date on the HH production
cross section and on the $\kappa_\mathrm{2V}$ coupling.
