Anisotropic Renyi holographic dark energy models in general relativity

•We construct Bianchi type-VI0 Renyi HDE models with Hubble and Granda-Oliveros horizons.•To investigate the physical behavior of the models, we obtain various cosmological parameters. The equation of state parameter shows quintom as well as phantom behavior of universe.•Model with Hubble horizon is stable and the model with Granda-Oliveros horizon is unstable.•Models exhibit the accelerated expansion of the universe and also correspond to Lambda CDM model.•The deceleration and equation of state parameters support recent observational data in both models. The purpose of this paper is to construct anisotropic and spatially homogeneous Bianchi type-VI0 Renyi holographic dark energy (RHDE) models in general relativity. For this purpose, we consider both Hubble and Granda-Oliveros horizons as IR cutoff. To obtain a deterministic solution of the field equations of the models we assume a relationship between the metric potentials which leads to an exponential solution and accelerated expansion. In order to investigate the physical behavior of our dark energy models, we obtain some important cosmological parameters like Hubble, deceleration, equation of state and statefinder as well as ωde-ωde′ planes. We also included the stability analysis for the dark energy models through the squared speed of sound. It is observed that the equation of state parameter shows quintom as well as the phantom behavior of universe. Also, the squared speed of sound gives the stability of RHDE model with Hubble horizon but unstable behavior for RHDE model with the Granda-Oliveros horizon. Statefinder diagnostic and deceleration parameters exhibit the accelerated expansion of the universe in both models and also correspond to the ΛCDM model at late times. The deceleration and equation of state parameters support recent observational data in both models.