Cosmic expansion and the merry-go-round
E.Bianchi and C.Rovelli (2010)

The Universe is expanding. And the expansion seems to be speeding up. To account for that acceleration, a mysterious factor, 'dark energy', is often invoked.

Is cosmic acceleration really a mystery? Many commentators have argued that it is, and that the explanation is to be found in invoking a mysterious substance, dark energy, that as yet has no theoretical underpinning. We disagree. An explanation is to hand and has been for many years. Cosmic acceleration is predicted and simply described by the theory of general relativity, together with a non-vanishing cosmological constant Λ.

The Λ cold dark matter (ΛCDM) cosmological model assumes the presence of Λ and is "almost universally accepted by cosmologists as the best description of the present data". Three objections to Λ are commonly presented, and nourish the 'mystery'. We argue that there is confusion - historical or conceptual - in each of them.

The first objection is known as 'Einstein's blunder'. Allegedly, Λ was rejected by general relativists, and indeed by Einstein himself, who first considered it but later called it his "greatest blunder". But Einstein's 'blunder' was not Λ. It was failing to see that - with or without Λ - the Universe isn't static in his theory of general relativity, thereby missing an easy prediction of the cosmic expansion before its discovery. Λ is not an appendage to Einstein's theory added to account for observations: it is an integral and natural part of it. Its nature and scale are no more or less mysterious than any of the several other constants in our fundamental theories.

The second objection is termed the 'coincidence problem'. Data indicate that we happen to live in a 'short' phase of cosmic history, during which the contributions from matter and Λ to the cosmic dynamics are comparable in magnitude. Such an 'unlikely coincidence' is presented as an argument against the ΛCDM hypothesis. But if the ratio of these contributions as a function of cosmic time is properly considered on a linear rather than a logarithmic scale, it can be seen that such a 'short' phase lasts for half the life of the Universe, and there is no 'unlikely' coincidence. In any case, we should not assume that we live in a fully random place or time in the Universe, as the coincidence-problem objection presupposes. The density around us, for instance, is very far from the average cosmic density.

The third objection concerns 'vacuum energy'. Quantum field theory (QFT) seems to predict a vacuum energy that adds to the cosmological force due to Λ - just as radiative corrections affect the charge of the electron. But this hypothetical contribution to Λ is much larger than the observed Λ. The discrepancy is an open puzzle in QFT in the presence of gravity. But it is a conceptual mistake to confuse Λ with QFT's vacuum energy. Λ cannot be reduced to the ill-understood effect of QFT's vacuum energy - or that of any other mysterious substance. Λ is a sort of 'zero-point curvature'; it is a repulsive force caused by the intrinsic dynamics of space-time.

Tests on the ΛCDM model must continue and alternative ideas must be explored. But it is our opinion - and that of many relativists - that saying dark energy is a 'great mystery', for a force explained by current theory, is misleading. It is especially wrong to talk about a substance. It is like attributing the force that pushes us out of a turning merry-go-round to a 'mysterious substance'.

From Nature 466 no.7304, E.Bianchi and C.Rovelli (2010)

ebianchi 2012