Abstract Recently, Falomir, Gamboa, Méndez, Gondolo and Maldonado proposed a bicosmology scenario for solving some cosmological problems related to inflation, dark matter, thermal history of the Universe (Falomir et al (2017 Phys. Rev. D 96 083534); Falomir (2018 Lett. B 785 399); (2020 Symmetry 12 435); Méndez (2021 103 123505)) . Their plan is introduce noncommutativity into momentum space tw...