Implications of an extended dark energy model with massive neutrinos

Recently there has been reports of finding a lower bound on the neutrino mass parameter ($\Sigma m_\nu$) when using ACT and SPTpol data however these bounds on the $\Sigma m_\nu$ are still weaker for most case around at 1 $\sigma$ level. In this context, here in this work, we study the consequences of using an enlarged four parameter dynamical dark energy equation of state on neutrino mass parameter as well as on the Hubble and S8 tensions. The four parameter dark energy equation of state incorporates a generic non-linear monotonic evolution of the dark energy equation of state, where the four parameters are the early and the present value of the equation of state, the transition scale factor and the sharpness of the transition. We report that with lensing-marginalized Planck + BAO + Pantheon and prior on absolute magnitude $M_B$ and KIDS/Viking $S_8$ prior, the model favours a non-zero value for the neutrino mass parameter at the most at $\sim 1 \sigma$ level ($\Sigma m_\nu = 0.1847_{-0.165}^{+0.0698}$ eV). In this case this model also brings down the Hubble tension to $\sim 2.5 \sigma$ level and the S8 tension to $\sim$ 1.5 $\sigma$ level. This model also provide a tighter constraints on the value of the dark energy equation of state at present epoch $w_0$ ($w_0 = -0.9901_{-0.0766}^{+0.0561}$) in comparison to the CPL like parameterization.