Search for neutrino masses in the Barrow holographic dark energy cosmology with Hubble horizon as IR cutoff

The Hubble IR cutoff in Barrow holographic dark energy in presence of neutrino masses using the latest observational data is investigated. The aim of this paper is twofold. At first we want to show that as it is well known, for spatially flat FRW cosmologies, the holographic dark energy disfavors the Hubble parameter as a candidate for the IR cutoff. We show that while the Hubble IR cutoff in standard holographic dark energy (HDE) prohibits accelerating expansion of the universe, the exponent parameter Δ in Barrow holographic dark energy (BHDE) significantly affect EoS parameter and under condition, Δ >Ω _m+2Ω _r/Ω _B , in (BHDE), the universe could experience accelerated expansion regime. The other is put constrain on ∑ m_ν , N_eff , Δ and the other parameters of the model using latest observational data. For this purpose, we employ the current cosmological observations, including the baryon acoustic oscillation measurements, the type Ia supernova data including Both Pantheon and Union2 data and the latest direct measurement of H_0 as well. Under the constraint of the all-data combination, we obtain ∑ m_ν<0.134 eV 95% CL and N_eff=2.92^+0.12_-0.12 68% CL which are in good agreement with Planck 2018 results. Also, we find the best value for exponent parameter as Δ =1.74^+0.25_-0.17 68% CL . For the best values of Δ and the other parameters of the model the EoS parameter shows the favored cosmological evolution for the universe which starts from the radiation dominated, passing the matter dominated and finally reaches the dark energy dominated. We also consider the holographic dark energy with interacting term Q=3β Hρ _B , for this case under the condition Δ -3β >Ω _m+2Ω _r/Ω _B the model can describe the late time acceleration of the Universe. For this case, we find Δ =0.52^+0.1_-0.08 and β =-0.15^+0.06_-0.06 68