Cycles of Time: An Extraordinary New View of the Universe

by Roger Penrose

evidence has mounted which strongly indicates that the expansion of the universe in its later stages does not actually match the evolution rates predicted from the standard Friedman cosmologies that are illustrated in Fig. 2.2. Instead, it appears that our universe has begun to accelerate in its expansion, at a rate that would be explained if we are to include into Einstein’s equations a cosmological constant Λ, with a small positive value. These, and later observations of various kinds,[2.11] have provided fairly convincing evidence of the beginnings of the exponential expansion characteristic of a Friedmann model with Λ>0. This exponential expansion occurs not only with the cases K≤0 which in any case expand indefinitely in their remote futures even when Λ=0, but also in the spatially closed case K>0, provided that Λ is large enough to overcome the tendency for recollapse that the closed Friedmann model possesses. Indeed, the evidence does indicate the presence of a large-enough Λ, so that the value (sign) of K has become more-or-less irrelevant to the expansion rate, where the (positive) value of Λ that appears actually to be present in Einstein’s equations would then dominate the late-time behaviour, providing an exponential expansion independently of the value of K within the observationally acceptable range.