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The measurement of $\Upsilon$(1S), $\Upsilon$(2S), and $\Upsilon$(3S) yieldsas a function of the charged-particle multiplicity density ${\rm d}N_{\rmch}/{\rm d}\eta$, using the ALICE experiment at the LHC, is reported in ppcollisions at $\sqrt{s}$ = 13 TeV. The $\Upsilon$ meson yields are measured atforward rapidity ($2.5 < y < 4$) in the dimuon decay channel, whereas thecharged-particle multiplicity is defined at central rapidity ($|\eta| < 1$).Both quantities are normalized to their average value in minimum bias events.The increase of the self-normalized $\Upsilon$(1S), $\Upsilon$(2S), and$\Upsilon$(3S) yields is found to be compatible with a linear scaling with theself-normalized ${\rm d}N_{\rm ch}/{\rm d}\eta$, within the uncertainties. Themeasured $\Upsilon$ excited-to-ground state self-normalized yield ratios arecompatible with unity within uncertainties. Similarly, the measured doubleratio of the self-normalized $\Upsilon$(1S) to the self-normalized J/$\psi$yields, both measured at forward rapidity, is compatible with unity forself-normalized charged-particle multiplicity beyond one. The measurements arecompared with theoretical predictions incorporating initial or final stateeffects.

Multiplicity dependence of $\Upsilon$ production at forward rapidity in pp collisions at $\sqrt{s}$ = 13 TeV