Theory of Dark Energy and Dark Matter (Journal of Mathematical Study, 2015)
In (T. Ma and S. Wang. Gravitational field equations and theory of darkmatter and dark energy, Discrete and Continuous Dynamical Systems, Ser. A, 34(2):335-366, 2014; arXiv:1206.5078v2), a new set of gravitational field equations are derivedbased only on 1) the Einstein principle of general relativity, and 2) the principleof interaction dynamics, due to the the presence of dark energy and dark matter. Withthe field equations, we show that gravity can display both attractive and repulsive behavior,and the dark matter and dark energy are just a property of gravity caused bythe nonlinear interactions of the gravitational potential $g_{μv}$ and its dual field. The mainobjectives of this paper are two-fold. The first is to study the PID-induced cosmologicalmodel, and to show explicitly, as addressed in (T. Ma and S. Wang, Astrophysicaldynamics and cosmology, Journal of Mathematical Study, 47(4): 305-378, 2014), that 1)dark matter is due to the curvature of space, and 2) dark energy corresponds to the negativepressure generated by the dual gravitational potential in the field equations, andmaintains the stability of geometry and large scale structure of the Universe. Second,for the gravitational field outside of a ball of centrally symmetric matter field, thereexist precisely two physical parameters dictating the two-dimensional stable manifoldof asymptotically flat space-time geometry, such that, as the distance to the center ofthe ball of the matter field increases, gravity behaves as Newtonian gravity, then additionalattraction due to the curvature of space (dark matter effect), and repulsive (darkenergy effect). This also clearly demonstrates that both dark matter and dark energyare just a property of gravity.