Abstract

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 A., which is related to the graviton mass via mg = h over bar /(A.c), that determines the range of the force and, finally, a Planck length quantity l0 that makes the potential regular at the centre. The modified 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 the Newton's constant as Geff = G (1 + alpha). Interestingly, we find an equation that relates the dark matter density, dark energy density, and baryonic matter density. It is given by S2D = root 2 S2BS2A(1 + z)3. 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 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 A.similar or equal to 103 [Mpc] and alpha similar or equal to 0.04, respectively. Finally, from these values, for the graviton mass, we get mg similar or equal to 10(-68) kg, and cosmological constant A similar or equal to 10(-52) m(-2). Further, we argue how this theory reproduces the MOND phenomenology on galactic scales via the acceleration of Milgrom a0 <^> 10-10 m/s2.(c) 2023 The Author(s). Published by Elsevier B.V.