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3.2.4 The cosmological constant Lambda

The cosmological constant lambda was introduced by Einstein (1917). It relates to the matter-density rho and is measured in units time-2. The cosmological constant used by Lemaître (1927) is related to matter-energy-density rho c2 and measured in units length-2, it is the same as the cosmological constant used today.

Einstein wrote:

``If it would then be certain, that the field equations which I have used so far, are the only ones in agreement with the postulate of the general theory of relativity, we must well conclude, that the theory of relativity does not admit the hypothesis of a spatial closure of the world.
. . . . We can, however, on the left-hand side of the field equations add the fundamental tensor gµv, multiplied with a presently unknown universal constant lambda, without disturbing the general covariance; we put in lieu of the field equations

Equation 36

The newly introduced universal constant lambda thus determines the average distribution density rho, which can remain in equilibrium, as well as the radius R of spherical space and its volume 2 pi2 R3.''

Einstein (1918):

``The G-field is determined entirely by the masses of the bodies. Since mass and energy are the same according to the results of the special theory of relativity and the energy is formally described by the symmetrical energy tensor (Tµv) this means, that the G-field be entirely caused and expressed by the energy tensor of matter.''

Einstein calls this postulate 'Mach's principle':

``I have chosen the name Mach's principle because this principle is a generalization of Mach's requirement that inertia must be interpreted as the interaction of bodies.
According to [the originally proposed field equations] a G-field would be possible without any generating matter, contrary to Mach's principle.
But the postulate is fulfilled - according to my present understanding - by field equations which are obtained by adding the lambda-term . . .
According to this equation a space-time continuum free from singularities with an everywhere disappearing energy tensor of matter seems not possible.``

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