STM-D-0858Paper2007Published and peer-reviewed

TASI Lectures on the Cosmological Constant

Raphael Bousso

Abstract and summary · read the original at the source

In one page

Raphael Bousso, of Berkeley and Lawrence Berkeley National Laboratory, gave these lectures to graduate students in 2007, and they remain the clearest short statement of why the weight of empty space is the sharpest open problem in physics. His opening move costs nothing: knowing only that the world is older than five thousand years and larger than Belgium already forces the cosmological constant to be tiny in natural units. Yet quantum field theory says the vacuum should weigh enormously more — electron loops alone overshoot by dozens of orders of magnitude, and so does every symmetry breaking in the standard model. Bousso then makes the point this site cares about most, in as few words as it can be made: dark energy is vacuum energy, and treating it as some other unknown substance is a habit, not a result. The measured density is about 3.2 times the density of matter. The second half sets out the one concrete candidate answer he sees, a vast discrete landscape of string-theory vacua.

Why it matters hereChapter 2 says the vacuum is a real medium carrying a real energy density, and chapter 13 asks how the whole picture fits together; this is the lecture course that states both halves of the tension in one place, from a theorist with no stake in the site’s conclusions. Its most useful sentence for a reader here is that dark energy is vacuum energy until something proves otherwise — the same identification the site makes — and its most useful number is the honest one: sixty to a hundred and twenty orders of magnitude, depending on where you cut the theory off, not a single headline figure.

What it claims

01The smallness of the cosmological constant can be deduced from elementary observations alone, with no precision cosmology at all: a positive value sets a horizon radius and a negative value forces recollapse, so any observed distance and any observed age bound it — and with distances and ages of order ten to the sixtieth in Planck units, the magnitude of Lambda is smaller than about three times ten to the minus one hundred and twenty.Section 1, Equations 1.2 to 1.5
Settled physics
02Quantum vacuum energy is indistinguishable from a cosmological constant and cannot be separated from it: Lorentz invariance forces the vacuum expectation value of the stress tensor to be proportional to the metric, so the bare constant in Einstein’s equation and the vacuum energy density of the fields can be absorbed into one another and only their sum is observable.Section 1, Equations 1.6 to 1.8
Settled physics
03Each known contribution to the vacuum energy overshoots the empirical bound of about ten to the minus one hundred and twenty-one by dozens of orders of magnitude — electron loops to a conservative 100 GeV cutoff give about ten to the minus sixty-eight in Planck units, a TeV supersymmetry-breaking cutoff at least ten to the minus sixty-four, electroweak symmetry breaking about ten to the minus sixty-seven, and QCD chiral symmetry breaking about ten to the minus seventy-nine — and these terms are uncorrelated with one another and with the bare constant.Section 1, the paragraphs following Equation 1.9, with Figure 1
Published and peer-reviewed
04Dark energy is vacuum energy: it is experimentally indistinguishable from vacuum energy and distinct from every other known form of matter, so treating it as something else turns one real problem into two, the second of which is an artefact of insisting that the vacuum energy must be exactly zero.Sections 5.1 and 5.2
Settled physics
05The measured value, from the 1998 supernova results and corroborated by the observed spatial flatness of the universe, is about one and a half times ten to the minus one hundred and twenty-three in Planck units — roughly 3.2 times the present matter density — which rules out theories driving the vacuum energy to zero and favours any theory predicting a value comparable to the matter density.Section 5, Equation 5.1
Settled physics
06A theory in which the vacuum energy varies from region to region can explain both its smallness and the coincidence that it is comparable to today’s matter density, and string theory supplies one: five-branes wrapping the hundreds of three-cycles of the compact extra dimensions give of order a hundred four-form fields, whose combinations pack the allowed vacuum energies densely enough that some vacuum lands in the narrow window where galaxies can form, out of perhaps ten to the five hundredth metastable vacua.Sections 4.1 to 4.3, 6.2 and 6.3, and Section 7
What to watch

Read it · abstract

Abstract

The energy density of the vacuum, Lambda, is at least 60 orders of magnitude smaller than several known contributions to it. Approaches to this problem are tightly constrained by data ranging from elementary observations to precision experiments. Absent overwhelming evidence to the contrary, dark energy can only be interpreted as vacuum energy, so the venerable assumption that Lambda=0 conflicts with observation. The possibility remains that Lambda is fundamentally variable, though constant over large spacetime regions. This can explain the observed value, but only in a theory satisfying a number of restrictive kinematic and dynamical conditions. String theory offers a concrete realization through its landscape of metastable vacua.

(Abstract only — see the rights note above. The full 39-page text is free to read at arXiv:0708.4231; the version of record is General Relativity and Gravitation 40, 607 to 637, doi:10.1007/s10714-007-0557-5. Bousso’s later colloquium-level account of the same subject is at /library/stm-8eb5f78376, and Steven Weinberg’s 1989 review — the argument these lectures build on — is at /library/stm-5610822bc8.)

The way in

https://arxiv.org/abs/0708.4231LICENCE CHECKED. The manuscript is arXiv:0708.4231, version 2 posted 11 September 2007, and the arXiv record carries the arXiv assumed-1991-2003 distribution grant rather than a Creative Commons licence — read on the arXiv abstract page on 2026-09-08 — and no Creative Commons statement appears in the text. So this sheet carries the summary, the claims and the author’s own abstract, and sends the reader to the source. Provenance from the paper’s own footnote 3: it is based on lectures given at the Theoretical Advanced Study Institute at the University of Colorado, Boulder, in May and June 2007, and was published under the shorter title ‘The cosmological constant’ in a special issue on dark energy of General Relativity and Gravitation, volume 40, pages 607 to 637, doi 10.1007/s10714-007-0557-5, online 11 December 2007 with the 2008 volume date — which is why the registry record carries 2008 while this sheet keeps 2007, the year of the lectures and of the manuscript whose title it uses. The claims below are read against the complete 39-page manuscript and the locators use its own section and equation numbering; numbers quoted in Planck units are the paper’s own, and exponents and inequalities are written out because the page is MDX. Bousso writes from the Center for Theoretical Physics and Department of Physics, University of California, Berkeley, and Lawrence Berkeley National Laboratory. REGISTRY NOTE: the record reached the library with chapters ch02, ch03 and ch13; chapter 3 is about inertia and gravity as zero-point-field effects, which these lectures do not treat, so the sheet carries chapters 2 and 13 — the same correction already made on the Weinberg and Martin sheets.

How to cite it

Raphael Bousso (2007) TASI Lectures on the Cosmological Constant. doi:10.1007/s10714-007-0557-5

Where it sits in the curriculum

What the vacuum is The unified picture