The cosmological Mass Varying Neutrino model in the late universe

Abstract: The cosmological Mass Varying Neutrino model beyond the standard $\Lambda$CDM scenario is considered. The interaction of the fermionic field and the scalar field with the inverse power law Ratra-Peebles potential via the Yukawa coupling is studied in detail. Depending on the model parameter $\alpha$ of the Ratra-Peebles potential of the scalar field, the expansion rate of the universe, the mass equation, the mass of the scalar field, the sum of neutrino masses, the mutual influence of the sum of neutrino masses and the value of the scalar field Ratra-Peebles potential as well as the total density of the thermodynamic potential of the coupled fermionic and scalar fields at the critical point are explored. The values of the sum of neutrino masses $m_\nu(a_0)\leq0.07~{\rm eV}$ calculated for values of the model parameter $\alpha$ of the Ratra-Peebles potential $0<\alpha\leq0.016$ are consistent with the constraint $m_\nu(a_0)<0.071~{\rm eV}$ of the cosmological DESI measurements, while the values $m_\nu(a_0)\leq0.45~{\rm eV}$ for $0<\alpha\leq0.143$ are consistent with the upper limit $m_\nu(a_0)<0.45~{\rm eV}$ obtained in the KATRIN experiment.