Bianchi type-III dark energy models with constant deceleration parameter in self-creation cosmology

We have constructed dark energy cosmological models in an anisotropic Bianchi type-III space–time with a variable equation of state (EoS) parameter ω in Barber’s (Gen. Relativ. Gravitation, 14, 117, 1982) second self-creation theory of gravitation. The models are obtained using the special law of variation of Hubble’s parameter that yields a constant value of the deceleration parameter. In the two different models that we have obtained, the EoS parameter ω for dark energy is found to be time dependent. In one model the value of ω is in good agreement with the recent observations of type Ia supernovae (SNe Ia) data, SNe Ia data with cosmic microwave background radiation anisotropy and galaxy clustering statistics. Further we have discussed the well-known astrophysical phenomena, namely, the Hubble parameter H(z), luminosity distance dL, proper distance d(z), distance modulus μ(z), and look-back time with red shift. The expression for jerk parameter and statefinder parameters are also derived.