Astoundingly, Einstein recanted his cosmological constant Λ when Hubble’s 1929 red shift calculations showed that the cosmos is not a static biblical “firmament” as was the prevailing proto-religious ideology in 1916, but was rather dynamic and expanding, and therefore Einstein’s Λ was no longer required to contort the lovely calculus of the GR field equations into Fred Hoyle’s static, spatially closed universe.
In 1922 Alexander Friedman—mentor to Sheldon Glashow—derived the Friedman Equation indicating that Einstein’s original GR field equations, before his insertion of Λ indicated that the universe was expanding, thus a contrived Λ theorem that precluded this expansion was wrong-headed. Even before Einstein’s 1931 formal renunciation of Λ, both relativistic cosmologist Arthur Eddington (The Expanding Universe, 1933), and Georges Lemaitre (Ann. Soc. Sci. Brux. 47:49 1927) retained it. Both agreed with Friedman that Einstein’s static universe (Λ>0) is unstable, and untenable and that Λ is indeed the necessary basis for a consistent cosmology.
Later Einstein referred to his insertion of the Λ term into the field equations as his “greatest blunder”. Why? Had he trusted the geometry of his wondrous field equations he would have predicted the expansion of the universe, and dark energy to boot, 13 years before Hubble’s great 1929 discovery. As Steven Weinberg might have said, he “did not take his mathematics seriously enough”.
Just so, the same could be said for the four marvelous equations of Maxwell that unified electricity and magnetism; and later of Dirac’s mathematical masterpiece that unified the quantum theory with Special Relativity (discovering antimatter in the process) to give us Relativistic Quantum Field Theory, the very ground of Feynman’s QED. It was perhaps Dirac’s cognitive reticence to trust his equations regarding antimatter that permitted later genius to steal his theoretical thunder.
Alas for the great mind that was Einstein, his hastily added, then retracted cosmological constant Λ, or something very like it is now back in the cosmic game as a ploy to make sense of “dark energy”. Dark energy is necessary to explain the recent discovery that the space of the universe is not only expanding, but accelerating exponentially. Platonic irony?
So it is, Einstein’s “greatest blunder”, the cosmological constant Λ has again arisen, phoenix-like, into the cosmological chess game. In 1980 Λ was proffered as the physical cause of the repulsive force of that great expansion—a trillionth of a second, give or take a trillionth, after a Big Bang singularity—that we now know and love as chaotic “inflation”. Again, the 1998 discovery of the repulsive dark energy that is hypothesized as the physical cause of the exponentially accelerating expanding cosmos has, as well, been attributed to Λ.
As we have seen, Einstein’s GR tells us that gravity is the curvature of spacetime. This curvature of space is the same everywhere, and the rate at which it expands throughout the expanding universe indicates its energy density. What is the topology of this curvature? We have three options. It may be negative, like a saddle, positive, like a sphere, or zero, flat. The current best guess based upon interpretations of the cosmic microwave background radiation (CMB)—the primordial energy remnants of the Big Bang—suggest that the actual curvature is approximately zero. The energy density of the universe then, the energy present in any volume of space, on the accord of GR, is a function of this curvature of space and its rate of expansion, probably infinite, ending in the high entropy “heat death” that is the frosty “Big Chill”.
So for Einstein’s GR the rate of expansion of the universe is relative to its overall energy density. It was the 1998 data from type Ia supernovae explosions that revealed this surprising acceleration of space, along with all of its galactic contents; which by the by, rescues us from the compactified fate of a contracting universal “Big Crunch” at the end of what may seem to be time.
“Empty space”—the vacuum of space—contains a small bit of fundamental energy. This tiny energy value is the cosmological constant Λ, usually known as the vacuum energy. As energy and matter are related by E=mc², GR predicts that Λ will have gravitational effects. Λ has a negative pressure that is equivalent to its energy density resulting in an accelerated expansion of the cosmos. Hence, the current Standard Model cosmological theory is known as the Lambda-CDM Model (cold dark matter) where lambda or Λ is the basal form of dark energy, and for now anyway, includes as its primary theorem Einstein’s cosmological constant Λ, a scalar field which comprises the energy density of a flat universe as a vacuum energy. Such current theory is supported by temperature anisotropy data from WMAP, and SDSS surveys of the redshift of distant galaxies (2002 to 2007).
Alternative explanations of mysterious dark energy include 1) several theories of “modified gravity” wherein Einstein’s GR gravity (the equivalence principal) is tweaked; and 2) the quintessence field. Quintessence is a hypothetical dynamical field, vis-á-vis the constant vacuum energy field, of a universal gradually changing energy density evolution. Thus quintessence differs from Λ for it is not constant but dynamic in space and time.
Non-baryonic dark matter by hypothesis is about 70 percent of the mass-energy density (remember E=mc²) of the cosmos. Dark matter—a neutral, uncharged non-interacting, or weakly interacting massive particle (wimp), not yet known to humanity—constitutes 25 percent; and fully 5 percent is baryonic (good old protons and neutrons) ordinary matter. One might well refer to such a Panglossian explanation of our wondrous cosmos as the Substandard Model of particles and forces, but that would be disrespectful.
So what, in heaven and earth, is the diabolical “cosmological constant problem”, first described by Steven Weinberg in 1989—later exclaimed by Leonard Susskind to be “the worst prediction ever….the mother of all physics problems”?
As seen above, the cosmological constant Λ, was introduced into the GR field equations by Einstein in 1917 (and later retracted) in order to defend his belief that the universe is static, while we now know that it is not only expanding, but accelerating exponentially. Λ is generally viewed as the zero point energy density of the quantum vacuum of space, the energy of space empty of all but virtual matter particles. This density was assumed to be zero (Λ=0).
The cosmological constant of 1998 is considered by cosmologists to be the current best physical explanation for dark energy, the repulsive force that is the cause for the expanding, accelerating universe. The bad news: theory seems to demonstrate that the value of this zero point energy is 120 orders of magnitude greater than what is actually observed! Such a value would inflate the universe at a rate that would preclude the formation of galaxies, and thus conscious observers to ponder the equation. Therefore this calculation must be incorrect. Hence the cosmological constant problem. This is indeed a physics sticky wicket.
What to do? Must we wait for a consistent quantum gravity theory? This requires profound changes to both of the “perfect theories” that are General Relativity and Relativistic Quantum Field Theory. We are led therefore to the multiverse.
Surely, a perfectly just and rational creator God, desirous of people to praise Him, would have no choice than to fine-tune a cosmological constant with a negative value, so that we might have an earth upon which to evolve and return to the light.
