An Oscillating Holographic Dark Energy in $f(R)$ Gravity

In this article, we investigated a Locally Rotationally Symmetric (LRS) Bianchi-II cosmological model with matter and Holographic Dark Energy (HDE) in the context of $f(R)$ theory of gravity. In order to find exact solutions to the field equations, we assumed that the Shear scalar $(\sigma)$ is proportional to Expansion scalar $(\theta)$. For HDE, it is observed that the Equation of state (EoS) parameter $\omega_{\Lambda}$ has an oscillating nature and lies in $[-0.778,\, 1.016].$ Also, we have studied the validity of energy conditions and shows that Null Energy Condition (NEC) is violated near the bouncing points. Moreover, we analysed the physical and geometrical aspects of the investigated model. Keywords: Holographic dark energy, LRS Bianchi-II, $f(R)$ gravity.