This proceeding presents the CMS searches for the nonresonant production of Higgs boson pairs in proton-proton collisions at a centre-of-mass energy of 13 TeV. The analyses use the full Run 2 dataset collected with the CMS detector during 2016–2018, corresponding to an integrated luminosity of 138 fb⁻¹. Several final states with complementary sensitivities are explored, including bbbb, bbττ, bbγγ, bbWW, bbZZ, multilepton, WWγγ, and ττγγ, together with a dedicated search for the associated production VHH → Vbbbb included in the global interpretation.

The observed (expected) upper limit on the inclusive Higgs boson pair production cross section relative to the Standard Model prediction is 3.5 (2.5) at 95% confidence level. Assuming all other Higgs boson couplings take their Standard Model values, the trilinear self-coupling modifier κₗ is constrained to −1.35 ≤ κₗ ≤ 6.37 at 95% confidence level. For the quartic vector-boson–Higgs coupling modifier, κ₂V = 0 is excluded with a significance of 6.6 standard deviations, with an allowed interval of 0.64 ≤ κ₂V ≤ 1.40 at 95% confidence level.

The results are interpreted within the Higgs Effective Field Theory, setting upper limits across established benchmarks and on the contact-interaction coefficient. An extrapolation to the integrated luminosity expected after the High-Luminosity LHC upgrade illustrates the projected improvement in sensitivity to nonresonant HH production and to the Higgs boson self-coupling. Combining single- and double-Higgs measurements further refines the determination of the trilinear coupling, with −1.2 < κₗ < 7.5 when other couplings are fixed and −1.4 < κₗ < 7.8 when they are allowed to vary.