Dark energy cosmological models with cosmic string

In this paper we have studied the anisotropic Kantowski-Sachs, locally rotationally symmetric (LRS) Bianchi type-I and LRS Bianchi type-III geometries filled with dark energy and one dimensional cosmic string in the Saez-Ballester theory of gravitation. To get physically valid solution we take hybrid expansion law of the average scale factor which is a product of power and exponential type of functions that results in time dependent deceleration parameter ( q ). The equation of state parameter of dark energy ( ω de ) has been discussed and we have observed that for the three models it crosses the phantom divide line ( ω de = − 1 ) and shows quintom like behavior. The density of dark energy ( ρ de ) is an increasing function of redshift and remains positive throughout the evolution of the universe for the three models. Moreover in Kantowski-Sachs and LRS Bianchi type-I geometries the dark energy density dominates the string tension density ( λ ) and proper density ( ρ ) throughout the evolution of the universe. The physical and geometrical aspects of the statefinder parameters ( r , s ), squared speed of sound ( v s 2 ) and ω de – ω de ′ plane are also discussed.