5.3. Challenges for quintessence

At the moment quintessence is viable but lacks clear motivation, and greater observational input is needed before it will be possible to decide if it is really along the right track. The supernova measurements so far are not capable of giving very serious constraints, but this will hopefully change in the near future, both by observations extending to higher redshift and by improved measurements and statistics both at redshifts approaching one, where most of the current data is, and in the local calibrating sample. One exciting prospect is a dedicated satellite project which is currently under consideration, which may allow current systematic errors to be addressed as well as delivering a vastly larger data set. Concerning non-supernova observations, improved constraints on parameters such as ₀, for instance from structure formation, would be welcome and will inform studies of quintessence. It may even eventually prove possible to spot the time evolution of quintessence by its effect on the microwave background through the integrated Sachs-Wolfe effect.

The two outstanding issues are the magnitude of the cosmological constant and why it should come to dominate at the present epoch. For a pure cosmological constant these are one and the same, and at present no lines of attack offer themselves. For quintessence, one question is whether there is an energy scale in fundamental physics comparable to the cosmological constant energy density (numerologists might consider for instance the similarity between the cosmological constant energy density and the measured neutrino mass-squared difference).

As to the coincidence problem, a very attractive, though as yet unrealized, notion is triggered quintessence, where the scalar field comes to dominate because a change in its behaviour is triggered by some other event. The obvious such recent event is matter-radiation equality, which occurred at a redshift of a few thousand. The ideal scenario would have perfect tracking during radiation domination, but a different behaviour during the matter era leading to domination after a suitable delay. At first sight, it seems that it might be possible to arrange this by coupling the quintessence field to the Ricci scalar, which vanishes in a perfect radiation dominated universe but is non-zero during matter domination. ⁽⁶⁾ Several such models have been studied [34], but unfortunately triggered quintessence has yet to be realised in a natural way and it is looking increasingly doubtful that this line of attack will prove fruitful.

⁶ Actually typically R is not zero during the radiation era, because it still receives a contribution from the subdominant matter which is actually larger than in the subsequent matter-dominated era. But R << H² is a more significant criterion which is true during the radiation era. Back.