The Cosmological Constant is Back
Lawrence M. Krauss · Michael S. Turner
Abstract and summary · read the original at the source
In one page
Three years before the supernova surveys measured it, Lawrence Krauss and Michael Turner wrote this short essay arguing that the universe must contain a cosmological constant, and that cosmologists should stop treating the idea as an embarrassment. Their case is a convergence rather than a single measurement. At the Hubble constant then favoured, the expansion age of a flat matter-only universe works out at about 8 billion years, while the oldest globular clusters were dated at 16 billion, give or take 3. Add the shape of large-scale structure and the mass inventory of galaxy clusters and each independent line points the same way. Their best fit puts matter at 30 to 40 per cent of the critical density and the cosmological constant at 60 to 70 per cent — close to the split measured today. Then they name the hard part. A cosmological constant is the energy density of the vacuum, and the value the observations want sits about 120 orders of magnitude below what quantum field theory predicts.
Why it matters hereChapter 2 treats the vacuum as a real medium with an energy density, and this is the paper that put that quantity back at the centre of cosmology — the cosmological constant and the zero-point energy of the vacuum named as one thing. Chapter 13 builds on exactly that identification, and chapter 1 uses the essay as a worked example of independent lines of evidence converging before any one of them is decisive.
What it claims
01A diverse set of observations — the age of the Universe, the formation of large-scale structure, and the matter content constrained by dynamical estimates, big-bang nucleosynthesis and cluster X-ray measurements — together require a nonzero cosmological constant; violating any single one of these constraints is not enough to allow a zero value, so unless at least two of the fundamental observations are incorrect the data demand it.Summary; the mass-density section, closing paragraph
Settled physics02The age problem is the most pressing piece of data: at a Hubble constant of 80 kilometres per second per megaparsec the expansion age of a flat matter-only universe is 8.2 billion years, and even taking a conservative matter density of 0.2 of critical it is only 10.4 billion, against oldest globular clusters dated at 16 plus or minus 3 billion years; a flat universe with matter at 0.2 and a cosmological constant at 0.8 of critical density gives 13.2 billion years instead.The age of the Universe section, pages 2 to 3
Published and peer-reviewed03In quantum field theory a nonzero cosmological constant is the energy density of the vacuum, and the numbers do not meet: fluctuations cut off at the Planck scale give about 10⁷⁶ GeV to the fourth, and about 10¹⁰ GeV to the fourth if supersymmetry lowers the cut-off to the weak scale, against the roughly 10⁻⁴⁶ GeV to the fourth the observations want — particle theorists have yet to constrain the value to within 50 orders of magnitude of the observational upper limit.The vacuum-energy section, pages 5 to 6
Settled physics04No symmetry principle has yet been found that guarantees a zero vacuum energy, and quantum-cosmological arguments for one rest on Euclidean quantum gravity; the authors note that whatever mechanism reduces the constant need not be an exact symmetry and may leave a small residue, with the wanted value close to a factor of the exponential of minus two over the fine-structure constant below the Planck density, and with Peccei–Quinn symmetry as a precedent for an imperfect cancellation of about 20 orders of magnitude.The cancellation-mechanism paragraphs, page 6
What to watch05The possibility the authors call the most intriguing is that the energy of the quantum vacuum is indeed zero and the Universe is currently in the middle of a phase transition, hung up in a false vacuum in a mild period of inflation; the energy scale of that transition would be about 0.003 electronvolts, close to neutrino masses postulated in some models and to the scale suggested by the solar neutrino problem.The late-time phase transition paragraph, page 6
What to watch06The authors name the measurements that would settle it: a definitive Hubble constant above about 75 kilometres per second per megaparsec would require a cosmological constant or the abandonment of big-bang cosmology, and the Hubble Space Telescope Key Project was then closing on 5 per cent accuracy; the geometry can also be read directly through gravitational lensing, galaxy number counts and angular sizes, and best of all through the distinctive distribution of the spherical-harmonic multipoles of the cosmic background radiation, which they expected to be measured within the decade.The detection-possibilities section, pages 6 to 7
What to watch
Read it · abstract
Abstract
A diverse set of observations now compellingly suggest that Universe possesses a nonzero cosmological constant. In the context of quantum-field theory a cosmological constant corresponds to the energy density of the vacuum, and the wanted value for the cosmological constant corresponds to a very tiny vacuum energy density. We discuss future observational tests for a cosmological constant as well as the fundamental theoretical challenges---and opportunities---that this poses for particle physics and for extending our understanding of the evolution of the Universe back to the earliest moments.
The way in
https://arxiv.org/abs/astro-ph/9504003arXiv:astro-ph/9504003, 3 April 1995; preprint numbers CWRU-P6-95 and FERMILAB-Pub-95/063-A; submitted to the Gravity Research Foundation Essay Competition and published as General Relativity and Gravitation 27, 1137–1144 (1995). The arXiv record carries the assumed-1991-2003 distribution grant rather than a Creative Commons licence, so this sheet reproduces the paper’s own summary and links to the source for the full text.
How to cite it
Lawrence M. Krauss, Michael S. Turner (1995) The Cosmological Constant is Back. doi:10.1007/BF02108229
Where it sits in the curriculum