Rényi holographic dark energy model with two IR cutoffs in Marder type universe

In the study of Saez–Ballester scalar tensor theory (Saez and Ballester in Phys Lett A 113:467, 1986), we examine the cosmic expansion phenomenon using the Rényi holographic dark energy (RHDE) with spatially homogeneous and anisotropic Marder type space time. Using a metric potential relationship, we find the solution to the field equations. Using Hubble and Granda–Oliveros horizon as IR cutoffs, we have derived the equation of state parameter (EoS) ( \(\omega _{de}\) ${\omega }_{\mathit{de}}$ ), RHDE energy density ( \(\rho _{de}\) ${\rho }_{\mathit{de}}$ ) and matter energy density ( \(\rho _{m}\) ${\rho }_m$ ), RHDE density parameter ( \(\Omega _{de}\) ${\mathrm{\Omega }}_{\mathit{de}}$ ), and Om-diagnostic. In this study, these parameters are plotted against the redshift (z). For three different choices of n and \(\delta\) $\delta$ , the EoS parameter exhibits quintom-like behavior for both IR cutoffs. Further, looking into the \(\omega _{de}-\omega _{de}'\) ${\omega }_{\mathit{de}}-{\omega }_{\mathit{de}}^{\prime }$ plane and stability of the DE model by using a metric perturbation method. It has been found that quintom-like behavior and freezing region explain the Universe’s accelerating rate of growth.