Assuming a universe that was static in time, and possessed of a uniform distribution of matter on the largest scales, Einstein was led to a finite, static universe of spherical spatial curvature.
To achieve a consistent solution to the Einstein field equations for the case of a static universe with a non-zero density of matter, Einstein found it necessary to introduce a new term to the field equations, the cosmological constant.
In the resulting model, the radius R and density of matter ρ of the universe were related to the cosmological constant Λ according to Λ = 1/R2 = κρ/2, where κ is the Einstein gravitational constant.
In both cases, he set the cosmological constant to zero, declaring it "no longer necessary ... and theoretically unsatisfactory".
The astrophysicist Mario Livio has recently cast doubt on this claim, suggesting that it may be exaggerated.