Dark Universe Phenomenology from Yukawa Potential?

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 $\lambda$, which is related to the graviton mass via $m_g=\hslash /(\lambda c)$, 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 $G_{\mathrm{eff}}\to G(1+\alpha )$. 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 $\Lambda \simeq 10^{-52}{\mathrm{m}}^{-2}$. Further, we argue how this theory reproduces the MOND phenomenology on galactic scales via the acceleration of Milgrom $a_0\simeq 10^{-10}m/{\mathrm{s}}^2$.

13 pages, 4 figures, final version

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• Black holes surrounded by massive vector fields in Kaluza-Klein gravity
• Probing black holes via quasinormal modes in a dark energy-induced dark matter
• VSL-Gravity in light of PSR B1913+16 Full Data Set: Upper limits on graviton mass and its theoretical consequences
• Limiting the Yukawa Gravity through the Black Hole Shadows of Sgr A* and M87*
• Revisiting the two-body problem in Yukawa gravity and in a gravitational extension of the Buckingham potential
• Gravitational Waves beyond the Linear Approximation and Gravitational Wave Reflection