AbstractThe production of $ϕ $ ϕ mesons has been studied in pp collisions at LHC energies with the ALICE detector via the dimuon decay channel in the rapidity region $2.5< y < 4$ 2.5 < y < 4 . Measurements of the differential cross section $\mathrm{d}^2σ /\mathrm{d}y \mathrm{d}p_{\mathrm {T}}$ d 2 σ / d y d p T are presented as a function of the transverse momentum ($p_{\mathrm {T}}$ p T ) at the center-of-mass energies $\sqrt{s}=5.02$ s = 5.02 , 8 and 13 TeV and compared with the ALICE results at midrapidity. The differential cross sections at $\sqrt{s}=5.02$ s = 5.02 and 13 TeV are also studied in several rapidity intervals as a function of $p_{\mathrm {T}}$ p T , and as a function of rapidity in three $p_{\mathrm {T}}$ p T intervals. A hardening of the $p_{\mathrm {T}}$ p T -differential cross section with the collision energy is observed, while, for a given energy, $p_{\mathrm {T}}$ p T spectra soften with increasing rapidity and, conversely, rapidity distributions get slightly narrower at increasing $p_{\mathrm {T}}$ p T . The new results, complementing the published measurements at $\sqrt{s}=2.76$ s = 2.76 and 7 TeV, allow one to establish the energy dependence of $ϕ $ ϕ meson production and to compare the measured cross sections with phenomenological models. None of the considered models manages to describe the evolution of the cross section with $p_{\mathrm {T}}$ p T and rapidity at all the energies.