An intensive search for a presumed “dark energy” driving the acceleration of the cosmic expansion has taken place during the past decade. Adjunct to the search is the determination of the acceleration's “equation of state” if the driver is other than λ, Einstein's cosmological constant. What is remarkable and long since forgotten is that Erwin Schrödinger, shortly after Albert Einstein introduced the cosmological constant, discussed the field equations without λ but with a stress-energy tensor containing the term . Einstein objected to this as a trivial variation of his field equations. It happened as follows.
Einstein introduced λ in 1917. 1 In November of that year, Schrödinger submitted a paper 2 in which Einstein's original equations, without λ, were provided with a stress-energy tensor consisting of a uniform distribution of dust and a negative pressure term. Shortly thereafter, in a note submitted to the same journal in March 1918, Einstein responded with some acerbity: 3
When I wrote my description of the cosmic gravitational field I naturally noticed, as the obvious possibility, the variant Herr Schrödinger had discussed. But I must confess that I did not consider this interpretation worthy of mention.
… A spatially closed world is only thinkable if the lines of force of gravitation, which end in ponderable bodies (stars), begin in empty space. Therefore, a modification of the theory is required such that “empty space” takes the role of gravitating, negative masses which are distributed all over the interstellar space. Herr Schrödinger now assumes the existence of matter with negative [scalar] mass density [negativen skalaren Massendichte] and represents it by the scalar p. This scalar p has nothing to do with the internal pressure of “really” ponderable masses, i.e., the noticeable pressure within stars of condensed matter of density ρ; ρ vanishes in the interstellar spaces, p does not.
The author [Schrödinger] is silent about the law according to which p should be determined as a function of the coordinates. We will consider only two possibilities:
p is a universal constant. In this case Herr Schrödinger's model completely agrees with mine. In order to see this, one merely needs to exchange the letter p with the letter λ and bring the corresponding term over to the left-hand side of the field equations. Therefore, this is not the case the author could have had in mind.
p is a variable. Then a differential equation is required which determines p as a function of x1 … x4. This means, one not only has to start out from the hypothesis of the existence of a nonobservable ne gative density in interstellar spaces but also has to postulate a hypothetical law about the space-time distribution of this mass density.
Of course, this occurred long before the advent of quantum-field theoretic concerns about zero-point energy and the later discovery of the type 1a supernovae with its implications, so the discussion vanished into the archives.
