Separate Einstein-Eddington Spaces and the Cosmological Constant

TL;DR

This paper derives a model of separate Einstein spaces with two cosmological constants from Eddington's affine variational principle, exploring implications for the universe's inflationary states and the cosmological constant problem.

Contribution

It introduces a novel affine variational framework leading to two separate Einstein spaces with potential zero cosmological constant, including scalar field effects.

Findings

Derivation of two maximally symmetric spaces with distinct cosmological constants.

Invariance under projections may set one cosmological constant to zero.

Model describes universe states before and after inflation.

Abstract

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.