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Based on Eddington affine variational principle on a locally product manifold, we derive the separate Einstein space described by its Ricci tensor. The derived field equations split into two field equations of motion that describe two maximally symmetric spaces with two cosmological constants. We argue that the invariance of the bi-field equations under projections on the separate spaces, may render one of the cosmological constants to zero. We also formulate the model in the presence of a scalar field. The resulted separate Einstein-Eddington spaces maybe considered as two states that describe the universe before and after inflation. A possibly interesting affine action for a general perfect fluid is also proposed. It turns out that the condition which leads to zero cosmological constant in the vacuum case, eliminates here the effects of the gravitational mass density of the perfect fluid, and the dynamic of the universe in its final state is governed by only the inertial mass density of the fluid.
We derive a model of dark energy which evolves with time via the scale factor. The equation of state $omega=(1-2alpha)/(1+2alpha)$ is studied as a function of a parameter $alpha$ introduced in this model. In addition to the recent accelerated expansi
In the Kaluza-Klein model with a cosmological constant and a flux, the external spacetime and its dimension of the created universe from a $S^s times S^{n-s}$ seed instanton can be identified in quantum cosmology. One can also show that in the intern
Self tuning is one of the few methods for dynamically cancelling a large cosmological constant and yet giving an accelerating universe. Its drawback is that it tends to screen all sources of energy density, including matter. We develop a model that t
Theoretically, the running of the cosmological constant in the IR region is not ruled out. On the other hand, from the QFT viewpoint, the energy released due to the variation of the cosmological constant in the late universe cannot go to the matter s
In this work we provide a link between a nearly vanishing cosmological constant and chiral symmetry. This is accomplished with a modification of General Relativity coupled to a topological field theory, namely BF theory by introducing fermions charge