Modified gravity emerging from thermodynamics and holographic principle
  A new conception is proposed in Ref.\cite{Verlinde:2010hp,Padmanabhan:2009kr}
that gravity is one kind of entropic force. In this letter, we try to discuss
its applications to the modified gravities by using three different corrections
to the area law of entropy which are derived from the quantum effects and extra
dimensions. According to the assumption of holographic principle, the number of
bits $N$ which is related to the equipartition law of energy is modified. Then,
the modified law of Newton's gravity and the modified Friedmann equations are
obtained by using the new notion. By choosing suitable parameters, the modified
area law of entropy leads to de-Sitter solutions which can be used to explain
the accelerating expansion of our universe. It suggests that the accelerating
phase in our universe may be an emergent phenomenon based on holographic
principle and thermodynamics.
