  We argue that the effect of cold dark matter in the cosmological setup can be
explained by the coupling between the baryonic matter particles in terms of the
long-range force having a graviton mass $m_g$ via the Yukawa gravitational
potential. Such a quantum-corrected Yukawa-like gravitational potential is
characterized by the coupling parameter $\alpha$, the wavelength parameter
$\lambda$, which is related to the graviton mass via $m_g=\hbar/(\lambda c)$,
that determines the range of the force and, finally, a Planck length quantity
$l_0$ that makes the potential regular at the centre. The corrected Friedmann
equations are obtained using Verlinde's entropic force interpretation of
gravity based on the holographic scenario and the equipartition law of energy.
The parameter $\alpha$ modifies Newton's constant as $G_{\rm eff}\rightarrow
G(1+\alpha)$. We argue that dark matter is an apparent effect as no dark matter
particle exists in this picture. Furthermore, the dark energy is also related
to graviton mass and $\alpha$; in particular, we point out that the
cosmological constant can be viewed as a self-interaction effect between
gravitons. We further show that there exists a precise correspondence with
Verlinde's emergent gravity theory, and due to the long-range force, the theory
can be viewed as a non-local gravity theory. To this end, we performed the
phase space analyses and estimated $\lambda\simeq 10^3 $[Mpc] and $\alpha \in
(0.0385,0.0450)$, respectively. Finally, from these values, for the graviton
mass, we get $m_g\simeq 10^{-68}$ kg, and cosmological constant $\Lambda \simeq
10^{-52}\rm m^{-2}$. Further, we argue how this theory reproduces the MOND
phenomenology on galactic scales via the acceleration of Milgrom $a_0 \simeq
10^{-10}\rm m/s^2$.
