Abstract <p>We investigate the cosmic progression of the Universe in the framework of Barber’s second self-creation (BSC) theory of gravitation in a non-interacting scenario with dark energy and dark matter. Using a Bianchi Type I metric in the self-creation of gravitation, we obtain the field equations that account for the presence of a cosmological constant. By considering the relationship between the average scale factor and Barber’s scalar field as a power law, solutions to these equations have been successfully obtained. Two assumed cosmic dynamics in the form of exponential expansion and power-law expansion are used to get the dark energy equation-of-state parameter. The effect of a polytropic equation of state on the physical quantities is studied. The role of the deceleration parameter and the effect of cosmic anisotropy on the cosmic dynamics are discussed.</p>