The Cosmological Constant
Sean M. Carroll
Abstract and summary · read the original at the source
In one page
Sean Carroll wrote this Living Review in 2001, at the moment the cosmological constant came back. He lays out what the constant is: a measure of the energy density of empty space, which general relativity treats as a perfect fluid whose pressure is the negative of its energy density, and which therefore pushes the universe apart instead of pulling it together. Then he does the arithmetic that has bothered physicists ever since. Add up what quantum field theory says should be sitting in the vacuum — the electroweak and QCD phase transitions, a grand-unification scale, zero-point fluctuations cut off at the Planck scale — and you get a number roughly 120 orders of magnitude larger than what the sky shows. On the observational side he walks through the two supernova teams, the microwave background, cluster masses and lensing, and finds them converging on a flat universe that is about seventy per cent vacuum energy and thirty per cent matter. His own verdict on that universe is the title of his last section: preposterous, and the best fit we have.
Why it matters hereChapter 2 turns on the identification Carroll spells out here — the cosmological constant and the energy of the vacuum are the same quantity — and this is the standard reference for it. Chapter 13 needs the honest ledger, and the gap between the vacuum energy the laboratory implies and the vacuum energy the sky measures is the largest open number in the whole picture.
What it claims
01The cosmological constant is a measure of the energy density of the vacuum. Because the only Lorentz-invariant form the vacuum energy-momentum tensor can take is one proportional to the metric, the vacuum behaves as a perfect fluid whose pressure is minus its energy density, and adding such a fluid to the Einstein equations is exactly equivalent to adding a cosmological constant. Carroll uses ’vacuum energy’ and ’cosmological constant’ interchangeably from that point on, and notes that the vacuum fluctuations themselves are very real, as evidenced by the Casimir effect.Section 1.3, Vacuum energy
Settled physics02The net vacuum energy is a sum of contributions that can each be estimated, and every estimate is enormous. The electroweak phase transition suggests a contribution set by a scale of about 200 giga-electronvolts, the breaking of chiral symmetry in the strong interactions a scale of about 0.3 giga-electronvolts, grand unification a scale near ten to the sixteenth giga-electronvolts, and zero-point fluctuations trusted up to the Planck scale a scale near ten to the eighteenth. Cosmological observation implies something far smaller, and the ratio is the famous discrepancy of 120 orders of magnitude. Carroll states plainly that no known symmetry enforces a vanishing vacuum energy, and calls this one of the most significant unsolved problems in fundamental physics.Section 1.3, Vacuum energy, closing paragraphs
What to watch03Two independent supernova searches reached the same answer. The High-Z Supernova Team and the Supernova Cosmology Project both favour a positive cosmological constant and strongly rule out the traditional flat matter-dominated universe. The method works because the peak brightness of a Type Ia supernova is tightly correlated with the shape of its light curve — dimmer events decline faster — which cuts the scatter in peak brightness from about 40 per cent to less than 15 per cent, enough to separate cosmological models.Section 3.1, Type Ia supernovae
Settled physics04The concordance is a flat universe of roughly thirty per cent matter and seventy per cent vacuum energy. Big-bang nucleosynthesis fixes the baryon share at about four per cent, so most of the matter is in some unknown non-baryonic form, and the largest single component of the universe is the energy of empty space.Section 5, Conclusions: The Preposterous Universe, first paragraph
Settled physics05The coincidence is the part Carroll finds hardest to swallow. Plot the vacuum fraction against the scale factor and it is negligible early and total late; we happen to observe from the brief cosmological era in which matter and vacuum are of comparable magnitude. He sets the challenge for the years after: work out whether these apparently distasteful features are surprising coincidences or a clue to a deeper structure not yet understood.Section 5, Conclusions: The Preposterous Universe, second and third paragraphs
What to watch06Dark energy need not be a constant. Any component that resists clustering on small scales and redshifts away only slowly will fit the data, and such a component is parameterised by an equation-of-state number running from zero for ordinary matter to minus one for a true cosmological constant. Supernovae, large-scale structure, lensing and the microwave background already favour a value near minus one, without closing off the others. The simplest dynamical alternative is quintessence, a single slowly rolling scalar field, and Carroll is careful that it brings its own naturalness problems: the field must be light enough to be rolling today, which by particle-physics standards is an incredibly small mass, and its couplings to ordinary matter must be suppressed by several orders of magnitude beyond what one would expect.Section 4.6, Other sources of dark energy
What to watch
Read it · abstract
Abstract
This is a review of the physics and cosmology of the cosmological constant. Focusing on recent developments, I present a pedagogical overview of cosmology in the presence of a cosmological constant, observational constraints on its magnitude, and the physics of a small (and potentially nonzero) vacuum energy.
Sean M. Carroll, Living Reviews in Relativity 4, 1 (2001), published 7 February 2001; preprint arXiv:astro-ph/0004075, 6 April 2000.
(Abstract only — see the rights note above. On this site, the essay that argued the case five years before the supernova results, Lawrence Krauss and Michael Turner’s The Cosmological Constant is Back, is at /library/stm-1b0b66c867, and Helge Kragh’s history of where the idea of a zero-point vacuum energy came from is at /library/stm-479f3334b8.)
The way in
https://arxiv.org/abs/astro-ph/0004075Published as Living Reviews in Relativity 4, 1 (2001), doi 10.12942/lrr-2001-1, and deposited in PubMed Central as PMC5256042. The preprint is arXiv:astro-ph/0004075, version 2 posted 8 April 2000, which carries the arXiv assumed-1991-2003 distribution grant rather than a Creative Commons licence — checked on the arXiv record on 2026-09-08 — and neither the version of record nor the PubMed Central deposit carries a Creative Commons statement; the deposit shows a bare author copyright line and no licence element. So this sheet holds the summary, the claims and the author’s own abstract and sends the reader to the source. The claims are read against the complete text of the review as deposited in PubMed Central, and the Living Review’s own section numbering is used in the locators. Sean M. Carroll wrote the review at the Enrico Fermi Institute and Department of Physics, University of Chicago; he is now at the California Institute of Technology.
How to cite it
Sean M. Carroll (2001) The Cosmological Constant. doi:10.12942/lrr-2001-1
Where it sits in the curriculum