Results of a search for non-resonant production of Higgs boson pairs decaying to two $\rm{b \bar{b}}$ pairs are presented. This search uses data from proton-proton collisions at a centre-of-mass energy of 13 TeV, collected by the CMS experiment at the LHC in 2016 and corresponding to an integrated luminosity of 35.9~\rm{fb}^{-1}. No signal is observed, and an upper limit of 847~\rm{fb} is set on the standard model cross section for non-resonant Higgs boson pair-production, where the Higgs bosons decay to $\rm{b \bar{b}}$ pairs. The same signature is studied in the context of theories of physics beyond the standard model that predict modified couplings of the Higgs boson, and used to extract limits on Higgs boson anomalous couplings.

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