Cosmology with Rotation in Hybrid Inflation

A cosmological scenario with dark energy (DE), rotation and hybrid inflation is proposed with the Bianchi type II metric. At the stage of early inflation, the decay of a double scalar field is considered, with a transition to the ultrarelativistic stage of the universe evolution. A solution to the Einstein equations and scalar field equations is found, together with the energy density and pressure components of an anisotropic fluid. A description of hybrid inflation with slow and fast rolling stages is obtained. The evolution of the rotation of DE, modeled by an anisotropic fluid, is investigated. We suppose that the anisotropic fluid does not transfer rotation to other types of matter, and at the Friedmann stages, it does not transfer rotation to produced matter particles. Then we obtain the result that if our scenario models the entire evolution of the Universe, assuming that the scale factor of the universe evolves as it inflates and then expands from the Planck value to the current size of the observable Universe, we can assume that in the modern era, the rotational velocity of the anisotropic fluid is of the order $$\omega_{c}=10^{-11}$$ /year. Important observations have been made on the application of our work with Sbytov and the results from the James Webb telescope in order to detect the possible rotation of the Universe.