Holographic dark matter and dark energy with second order invariants

One of the main goals of modern cosmology remains to summon up a self-consistent policy, able to explain, in the framework of Einstein's theory, the cosmic speedup and the presence of dark matter in the Universe. According to the holographic principle, which postulates the existence of a minimal size of a physical region, we argue, in this paper, that if this size exists for the Universe and it is accrued from the independent geometrical second order invariants, it would be possible to ensure a surprising source for dark matter and a viable candidate for explaining the late acceleration of the Universe. We develop low redshift tests, such as supernovae Ia and kinematical analysis, compiled by the use of cosmography, and we compare the outcomes with higher redshift tests, such as the CMB peak and anisotropy of the cosmic power spectrum. All the results indicate that the models presented here can be interpreted as unified models that are capable of describing both dark matter and dark energy.