This paper, written together with Alexei Starobinsky, was the first comprehensive review on the cosmological constant and the nature of dark energy after the discovery of the acceleration of our Universe (in 1998). The paper reviewed the observational situation and summarized the scientific grounds for acceleration; it also provided a detailed account of the cosmological constant—the historical development of this idea and the possible origin of a cosmological constant from vacuum fluctuations. The paper also discussed the advantages and shortcomings of dynamical models describing acceleration. It was comprehensive and had a pedagogical narrative which made it accessible to a large audience, including professional researchers as well as graduate and undergraduate students.

The possibility that our universe may be accelerating is one of the key observational discoveries of this decade. The Einstein equations—which so well describe our local Universe—state that in the presence of "normal'' matter, the Universe should decelerate rather than accelerate. By "normal'' one means matter with non-negative pressure. Indeed almost all examples of matter known in the laboratory have this property. According to the Einstein equations the Universe will accelerate only if it is dominated by an unusual form of matter having large negative pressure. The best (theoretical) example of such form of matter is furnished by a cosmological constant which describes the quantum properties of the vacuum. However this "vacuum energy,'' if it exists, is predicted to be many orders of magnitude larger than the value of the cosmological constant inferred from the acceleration of the Universe. This mismatch has often been referred to as the "cosmological constant problem". The cosmological constant also suffers from a "fine tuning problem'' since its value must be set far below any natural scale (at early times) in order that its presence is felt at precisely the present epoch. A larger value of the cosmological constant gives rise to a Universe which begins to accelerate much too soon, in such a Universe galaxy formation is strongly suppressed, and therefore it does not resemble our own. To alleviate this problem dynamical models called "dark energy'' or "quintessence" have been proposed. In these models the acceleration of the Universe is a recent phenomenon which arises because the dark energy evolves dynamically from a large initial value to small present day values. By contrast the value of a cosmological constant, as its name suggests, remains "fixed" at all times. The paper reviews dark energy models and discusses how the equation of state of dark energy can be reconstructed from observations of high redshift type Ia supernovae as well as other (complementary) sets of observations.

I was writing a theoretical paper with Salman Habib (subsequently published in Phys.Rev.Lett.), in which the Universe was driven to accelerate by quantum effects, when I became aware of supernova observations supporting an accelerating Universe. After the publication of the Phys.Rev.Lett. paper I was invited by the editors of IJMP to write a review for their journal in which the case for an accelerating Universe was discussed at some length and both theoretical as well as observational issues were reviewed. This review was subsequently written with Alexei Starobinsky, and I have followed it up with a dozen or so other papers in which the properties of dark energy have been carefully researched and compared against observations.