R\' enyi Holographic Dark Energy in Higher Dimension Cosmology

R\'enyi holographic dark energy (RHDE) correspondence is discussed in higher dimensional cosmology, namely Kaluza-Klein (KK) cosmology. Both interacting and non-interacting cosmological scenario are considered here. It is found that the non-interacting model naturally leads to the late accelerated universe, unlike the standard Holographic Dark Energy models in 4$D$, which requires interaction to accommodate the late-time acceleration of the universe. The interacting model produces an accelerating universe at late time albeit failing to attain the estimated present value of the deceleration parameter. The evolution of different cosmologically relevant parameters have been estimated. We consider here two diagnostic tests namely, state-finder and $Om$ diagnostics to study the non-interacting model which is more favoured in the light of recent cosmological observations. Classical stability of the cosmological models are also discussed