Holographic Theory of Gravity and Cosmology
  According to the holographic principle, the maximum amount of information
stored in a region of space scales as the area of its two-dimensional surface,
like a hologram. We show that the holographic principle can be understood
heuristically as originated from quantum fluctuations of spacetime. Applied to
cosmology, this consideration leads to a dynamical cosmological constant
$\Lambda$ of the observed magnitude, in agreement with the result obtained for
the present and recent cosmic eras, by using unimodular gravity and causal-set
theory. By generalizing the concept of entropic gravity, we find a critical
acceleration parameter related to $\Lambda$ in galactic dynamics, and we
construct a phenomenological model of dark matter which we call "modified dark
matter" (MDM). We provide successful observational tests of MDM at both the
galactic and cluster scales. We also discuss the possibility that the quanta of
both dark energy and dark matter obey the quantum Boltzmann statistics or
infinite statistics as described by a curious average of the bosonic and
fermionic algebras.
