Apparent dark matter inspired by the Einstein equation of state

The purpose of this article is twofold. First, by means of Padmanabhan's proposal on the emergence nature of gravity, we recover the ΛCDM model and the effect of the dark matter in the context of cosmology. Toward this goal, we use the key idea of Padmanabhan that states cosmic space emerges as the cosmic time progresses and links the emergence of space to the difference between the number of degrees of freedom on the boundary and in the bulk. Interestingly enough, we show that the effect of the cold dark matter in the cosmological setup can be understood by assuming an interaction between the numbers of degrees of freedom in the bulk. In the second part, we follow Jacobson's argument and obtain the modified Einstein field equations with additional dark matter component emerging due to the interaction term between dark energy and baryonic matter related by , where α is a coupling constant. Finally, a correspondence with the Yukawa cosmology is pointed out, and the role of massive gravitons as a possibility in explaining the nature of the dark sector as well as the theoretical origin of the Modified Newtonian Dynamics (MOND) are addressed. We speculate that the interaction coupling α fundamentally measures the entanglement between the gravitons and matter fields and there exists a fundamental limitation in measuring the gravitons wavelength.