  The effects of the isovector-scalar $\delta$-meson field on the properties of
finite nuclei, infinite nuclear matter and neutron stars are investigated
within the Relativistic Mean Field (RMF) model which includes non-linear
couplings. Several parameter sets (SRV's) are generated to asses the influence
of $\delta$-meson on the properties of neutron star. These parametrizations
correspond to different values of coupling constant of $\delta$-meson to the
nucleons with remaining ones calibrated to yield finite nuclei and infinite
nuclear matter properties consistent with the available experimental data. It
is observed that to fit the properties of finite nuclei and infinite nuclear
matter, a stronger coupling between isovector-vector $\rho$ meson and nucleons
is required in the presence of $\delta$ field. Furthermore, the $\delta$-meson
is found to affect the radius of canonical neutron star significantly. The
value of dimensionless tidal deformability, ${\Lambda}$ for the canonical
neutron star also satisfies the constraints from the waveform models analysis
of GW170817 binary neutron star merger event. A covariance analysis is
performed to estimate the statistical uncertainties of the model parameters as
well as correlations among the model parameters and different observables of
interest.
