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.Comment: Accepted in Annalen der Physik journal. 7 pages, typos correcte
