Renyi Holographic dark energy models in Saez-Ballester theory of gravitation

Abstract We construct anisotropic and spatially homogeneous Renyi holographic dark energy (RHDE) models in this research's Saez and Ballester scalar-tensor of gravity. As IR cutoff, we examine both the Hubble and Granda Oliveros horizons. To provide a deterministic solution to the model's field equations, we assume a relationship of the metric potentials, which results in an accelerated expansion. We get several crucial cosmological parameters such as Hubble, deceleration, and Equation of state, as well as \({w}_{de}- {w}_{de}^{{\prime }}\) planes, to explore the physical behaviour of our dark energy models. Furthermore, the squared speed of sound provides stability for the RHDE model with the Hubble horizon but unstable behaviour for the RHDE model with the Granda-Oliveros horizon. In both models, State finder diagnostic and the deceleration parameters represents the rapid expansion of the cosmos and corresponds to the \({\Lambda }\)CDM model.