Quantum gravity refers to a theory yet to be discovered that unites quantum mechanics with classical general relativity. At present gravity stands outside the Standard Model of particle physics, which is a deeply unsatisfactory situation. The current paradigm is that the universe began as a singularity that expanded rapidly. There is a fleeting moment in this expansion when the self-gravity of the universe is the dominant force. Without a good theory of quantum gravity we cannot understand this singularity or its properties or the initial expansion. In short, we don’t know anything about the properties of the earliest universe.

A barrier to understanding string cosmology is first to gain a better understanding of string theory, and that’s what paper #3 is grasping for. String theories and M theory both appear to be limiting cases of a more powerful theory. At the heart of string theory is the concept of small hidden dimensions. String theory has six extra spatial dimensions, and M theory has seven. These are required to make the quantum features of the theory consistent. But the properties of these pesky extra dimensions are themselves evolving in time, which adds great mathematical complexity.

As the title of #3 suggests, string theorists are taking a lively interest in de Sitter spaces, or vacua. Willem de Sitter (1872–1934) was a mathematical astronomer who became a pioneer in exploring the astronomical implications of general relativity. The Dutch theorist found a solution of Einstein’s equations that permitted a stable, empty, expanding universe. He correctly predicted that in such a space the galaxies at great distances would show high redshifts. This classical solution had the additional merit of maximal symmetry. The current generation of theorists believe that we may well be living in a de Sitter space. A further motivation for working in de Sitter space is that it offers a means of quantizing general relativity.

Most research on string cosmology has danced around the edge of the landscape where classical solutions apply. The bold step taken by Shamit Kachru and three Stanford University colleagues is to burst into the quantum wilderness of string theory. Paper #3 is saying that quantum effects can lead to realistic cosmology, and that’s certainly a step in a promising direction. In the Stanford construction 6 of the 10 dimensions are made compact. They add a small dose of 3-D branes to break supersymmetry and to lift the construct into the realm of de Sitter space. Then a little fine-tuning produces a space with accelerating expansion (positive cosmological constant). This is the most astonishing breakthrough, and to appreciate its significance we must turn to Hot Papers #1 and #2.

With 1,058 citations, #1 is now the most highly cited paper across all of science for the last 18 months. Both #1 and #2 give values for the cosmological parameters with such precision that it is now possible to speak of a Standard Model: a flat universe, undergoing an accelerating expansion, and containing ordinary matter, dark matter, and dark energy. The most unexpected feature is the acceleration, a property that Einstein anticipated but subsequently ignored as his "greatest mistake." Less than 5% of the universe is observable matter. Most of it is dark matter or dark energy, the latter being required to drive the expansion. Now we have string theory giving an explanation of this acceleration.