Minimal Length, Friedmann Equations and Maximum Density
  Inspired by Jacobson's thermodynamic approach[gr-qc/9504004], Cai et al
[hep-th/0501055,hep-th/0609128] have shown the emergence of Friedmann equations
from the first law of thermodynamics. We extend Akbar--Cai derivation
[hep-th/0609128] of Friedmann equations to accommodate a general entropy-area
law. Studying the resulted Friedmann equations using a specific entropy-area
law, which is motivated by the generalized uncertainty principle (GUP), reveals
the existence of a maximum energy density closed to Planck density. Allowing
for a general continuous pressure $p(\rho,a)$ leads to bounded curvature
invariants and a general nonsingular evolution. In this case, the maximum
energy density is reached in a finite time and there is no cosmological
evolution beyond this point which leaves the big bang singularity inaccessible
from a spacetime prospective. The existence of maximum energy density and a
general nonsingular evolution is independent of the equation of state and the
spacial curvature $k$. As an example we study the evolution of the equation of
state $p=\omega \rho$ through its phase-space diagram to show the existence of
a maximum energy which is reachable in a finite time.
