The minimal GUT with inflaton and dark matter unification

Giving up the solutions to the fine-tuning problems, we propose the non-supersymmetric flipped $$SU(5)\times U(1)_X$$ model based on the minimal particle content principle, which can be constructed from the four-dimensional SO(10) models, five-dimensional orbifold SO(10) models, and local F-theory SO(10) models. To achieve gauge coupling unification, we introduce one pair of vector-like fermions, which form a complete $$SU(5)\times U(1)_X$$ representation. The proton lifetime is around $$5\times 10^{35}$$ years, neutrino masses and mixing can be explained via the seesaw mechanism, baryon asymmetry can be generated via leptogenesis, and the vacuum stability problem can be solved as well. In particular, we propose that inflaton and dark matter particles can be unified to a real scalar field with $$Z_2$$ symmetry, which is not an axion and does not have the non-minimal coupling to gravity. Such a kind of scenarios can be applied to the generic scalar dark matter models. Also, we find that the vector-like particle corrections to the $$B_s^0$$ masses might be about 6.6%, while their corrections to the $$K^0$$ and $$B_d^0$$ masses are negligible.