Gravitation And Emergence Of Space

Since the discovery of black hole thermodynamics, which implies that there may be deep connections between gravitational systems and thermodynamical systems, physicists have been speculating that gravity may not be a fundamental interaction but an emergent phenomenon. When Jacobson derived Einstein field equations by applying the Clausius relation on a local Rindler causal horizon in 1995, the guess became more concrete. On the other hand, by studying the entropy of black holes, Susskind and ’t Hooft proposed the holographic principle which states that there is a correspondence between the degrees of freedom (DOF) of a gravitational system and those of the boundary. Now the holographic principle is thought to possibly be a fundamental principle of quantum gravity. Also, it provides a reasonable evidence of emergent gravity. Recently, Padmanabhan applied the emergent perspective of gravity to cosmology. By arguing that the spacial expansion of our universe is due to the difference between the surface DOF and the bulk DOF in a region of emerged space, which is the equipartition principle called by Padmanabhan, he finally derived the Friedmann equation of a Friedmann-Robertson-Walker (FRW) universe when the equipartition is applied on the Hubble horizon.The derivation process can be generalized to higher dimensional Einstein gravity, Gauss-Bonnet gravity and more general Lovelock gravity with different modifications of Padmanab-han’s proposed equation. From another viewpoint, these modifications can be thought to replace the difference of the surface DOF and the bulk DOF by its function while the formula is kept fixed. This point of view is called the generalized equipartition. Nonetheless, one can obtain the Friedmann equations in a only flat FRW universe from these generalizations. For obtaining the Friedmann equations of a FRW universe with any spacial curvature, one need to further modify the formula and apply it to the apparent horizon.By considering the generalizations mentioned above, we proposed a general formula. Those modifications can be treated as special cases of this formula. Moreover, we investigat- ed the dynamic equations of a FRW universe in the f(R) theory and deformed Horava-Lifshitz theory using the proposed formula. With the idea proposed by Padmanabhan, we obtained the modified dynamic equations from the perspective of emergent phenomena. The resulting equa-tions show a strong consistency with the standard Friedmann equation of the FRW universe in general relativity when n= 3, f(R)= R and ωâ†' 0.On the other hand, for obtaining the Friedmann equations of a FRW univese with any spacial curvature in higher dimensional gravity, Gauss-Bonnet gravity and Lovelock gravity, we applied the generalized equipartition on the apparent horizon and derived the different ex-pressions relate to different gravity theories. We concluded that the failure of obtaining the Friedmann equations with any spacial curvature when the generalized equipartition is applied on the Hubble horizon implies that it actually holds for the apparent horizon and no longer for the Hubble horizon in these gravity theories.As Padmanabhan said, the new perspective provides a different paradigm to study cosmol-ogy. We finally studied the de Sitter universe with this approach. We got strong constraints of state parameter and energy density in a de Sitter universe when the equipartition is satisfied. It may provides a guide when one study the early time de Sitter phase of the FRW universe caused by inflation and the late time de Sitter phase caused by dynamical dark energy.