  In Verlinde's entropic force scenario of gravity, Newton's laws and Einstein
equations can be obtained from the first pinciples and general assumptions.
However, the equipartition law of energy is invalid at very low temperatures.
We show clearly that the threshold of the equipartition law of energy is
related with horizon of the universe. Thus, a one-dimension Debye (ODD) model
in the direction of radius of the modified entropic force (MEF) maybe suitable
in description of the accelerated expanding universe. We present a Friedmann
cosmic dynamical model in the ODD-MEF framework. We examine carefully
constraints on the ODD-MEF model from the Union2 compilation of the Supernova
Cosmology Project (SCP) collaboration, the data from the observation of the
large-scale structure (LSS) and the cosmic microwave background (CMB), i.e. SNe
Ia+LSS+CMB. The combined numerical analysis gives the best-fit value of the
model parameters $\zeta\simeq10^{-9}$ and $\Omega_{m0}=0.224$, with
$\chi_{min}^2=591.156$. The corresponding age of the universe agrees with the
result of D. Spergel {\it et al.}\cite{Spergel2003} at 95% confidence level.
The numerical result also yields an accelerated expanding universe without
invoking any kind of dark energy. Taking $\zeta(\equiv 2\pi \omega_D/H_0)$ as a
running parameter associated with the structure scale $r$, we obtain a possible
unified scenario of the asymptotic flatness of the radial velocity dispersion
of spiral galaxies, the accelerated expanding universe and the Pioneer 10/11
anomaly in the entropic force framework of Verlinde.
