Historical research guide · 0858 · 2007
TASI Lectures on the Cosmological Constant
Raphael Bousso
In one minute
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.
Connection
Chapter 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.
From the source
The 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
Quantum 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
Each 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
Dark 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
The 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
A 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
The way in
https://arxiv.org/abs/0708.4231How to cite it
Raphael Bousso (2007) TASI Lectures on the Cosmological Constant doi:10.1007/s10714-007-0557-5