  In this work, we propose the Ricci-cubic holographic dark energy model. The
model is inspired by the cubic curvature invariant formed by the contraction of
three Riemann tensors. A combination of Ricci scalar and the cubic invariant is
used to describe the infrared cutoff of the holographic dark energy. Such a
construction is extremely useful since the evolution does not depend on the
past or future features of the universe, but completely on its present
features. Moreover, the use of invariants makes the theory more fundamental in
nature. We have constructed the model and studied its cosmological features.
The analytical solutions of various cosmological parameters such as the density
parameter, equation of state parameter, and deceleration parameter are
extracted and their behaviour is studied. It is seen that the holographic dark
energy model can exhibit the entire thermal history of the universe,
sequentially starting from radiation in the early universe, followed by matter,
and finally the dark energy dominated epoch at late times. The equation of
state parameter shows that the model can exhibit quintessence nature,
phantom-divide crossing, and even phantom nature depending on the choice of
parameter spaces.
