Constraining parameters of spinor field dark energy: An alternative to $\Lambda$CDM model under the spherically symmetric FLRW space-time

This study constrains the cosmological parameters within the scope of a spherically symmetric FLRW cosmological model, the role of a nonlinear spinor field in the universe's evolution. To test this approach, we incorporate the recent Cosmic chronometers, Supernova, and Sloan Digital Sky Survey data. It is found that if spherical coordinates give the FLRW model, the energy-momentum tensor (EMT) of the spinor field possesses nontrivial non-diagonal components. These non-diagonal components of EMT neither depend on the spinor field nonlinearity nor the value of the parameter $k$ defining the type of curvature of the FLRW model. In this context, we construct a dark energy model and perform an MCMC simulation to obtain the best-fit values of the parameters. The results are well comparable to the present Hubble parameter and deceleration parameter, indicating the accelerated expansion of the universe.