C. Some explanations

We have to explain our choice of nomenclature. Basic concepts of physics say space contains homogeneous zero-point energy, and maybe also energy that is homogeneous or nearly so in other forms, real or effective (as from counter terms in the gravity physics, which make the net energy density cosmologically acceptable). In the literature this near homogeneous energy has been termed the vacuum energy, the sum of vacuum energy and quintessence (Caldwell, Davé, and Steinhardt, 1998), and the dark energy (Turner, 1999). We have adopted the last term, and we will refer to the dark energy density that manifests itself as an effective version of Einstein's cosmological constant, but one that may vary slowly with time and position. ⁽⁶⁾

Our subject involves two quite different traditions, in physics and astronomy. Each has familiar notation, and familiar ideas that may be "in the air" but not in the recent literature. Our attempt to take account of these traditions commences with the summary in Sec. II of the basic notation with brief explanations. We expect readers will find some of these concepts trivial and others of some use, and that the useful parts will be different for different readers.

We offer in Sec. III our reading of the history of ideas on and its generalization to dark energy. This is a fascinating and we think edifying illustration of how science may advance in unexpected directions. It is relevant to an understanding of the present state of research in cosmology, because traditions inform opinions, and people have had mixed feelings about ever since Einstein (1917) introduced it 85 years ago. The concept never entirely dropped out of sight in cosmology because a series of observations hinted at its presence, and because to some cosmologists fits the formalism too well to be ignored. The search for the physics of the vacuum, and its possible relation to , has a long history too. Despite the common and strong suspicion that must be negligibly small, because any other acceptable value is absurd, all this history has made the community well prepared for the recent observational developments that argue for the detection of .

Our approach in Sec. IV to the discussion of the evidence for detection of , from the cosmological tests, also requires explanation. One occasionally reads that the tests will show us how the world ends. That certainly seems interesting, but it is not the main point: why should we trust an extrapolation into the indefinite future of a theory we can at best show is a good approximation to reality? ⁽⁷⁾ As we remarked in Sec. I.A, the purpose of the tests is to check the approximation to reality, by checking the physics and astronomy of the standard relativistic cosmological model, along with any viable alternatives that may be discovered. We take our task to be to identify the aspects of the standard theory that enter the interpretation of the measurements and thus are or may be empirically checked or measured.

⁶ The dark energy should of course be distinguished from a hypothetical gas of particles with velocity dispersion large enough that the distribution is close to homogeneous. Back.

⁷ Observations may now have detected , at a characteristic energy scale of a millielectronvolt (Eq. [47]). We have no guarantee that there is not an even lower energy scale; such a scale could first become apparent through the cosmological tests. Back.