  Some time ago, it has been suggested that gravitons can acquire mass in the
process of spontaneous symmetry breaking of diffeomorphisms through the
condensation of scalar fields [Chamseddine and Mukhanov, JHEP, 2010]. Taking
this possibility into account, in the present paper, first we show how the
graviton mass intricately reshapes the gravitational potential akin to a
Yukawa-like potential at large distances. Notably, this long-range force
modifies the Newton's law in large distances and might explain the phenomena of
dark matter. The most important finding in the present paper is the derivation
of a modified Newtons law of gravity by modifying the Verlindes entropic force
relation due to the graviton contribution. The graviton contribution to the
entropy basically measures the correlation of graviton and matter fields which
then reproduces the Bekenstein-Hawking entropy at the horizon. This result
shows the dual description of gravity: in the language of quantum information
and entropy the gravity can be viewed as an entropic force, however in terms of
particles and fields, it can be viewed as a longe range force. Further we have
recovered the corrected Einstein field equations as well as the $\Lambda$CDM
where dark matter emerges as an apparent effect.
