The Cosmological Constant Problem, Dark Energy, and the Landscape of String Theory
Raphael Bousso
Abstract and summary · read the original at the source
In one page
Raphael Bousso, at Berkeley, wrote this one as a colloquium: the cosmological constant problem explained so that a graduate student, or a patient reader, can follow it end to end. His first point is that the energy of empty space is not optional. Every mode of every field carries a zero-point energy, and Bousso says plainly that we know vacuum energy exists in nature because we can change how much of it sits inside a bounded region, in Casimir-type experiments. His second point is the size of the mismatch: the sky measures a vacuum energy of about 1.35 times ten to the minus one hundred and twenty-third in Planck units, at least sixty orders of magnitude below what the Standard Model’s own known contributions add up to. His third is that the dark energy driving cosmic acceleration is almost certainly that same vacuum energy, not a new fluid and not a change to gravity. The second half offers a speculative resolution: string theory’s landscape of vacua, populated by eternal inflation.
Why it matters hereChapter 2 rests on the statement that empty space carries a real energy density, and this is that statement made by a mainstream cosmologist in the plainest terms available — vacuum energy exists, it is measurable, and it is what the accelerating universe is made of. Chapter 13 needs the ledger of the gap between the laboratory number and the sky number kept honestly, and Bousso keeps it at sixty orders and up rather than reaching for the largest figure available. Read alongside Steven Weinberg’s 1989 review at /library/stm-5610822bc8, which turned this into the problem everyone knows by name, and Jérôme Martin’s 2012 account at /library/stm-568da33759, which shows how to quote the size of the gap without handing a critic a free win.
What it claims
01The vacuum has an energy density like any physical object, and Lorentz invariance forces its stress tensor to be proportional to the metric. What distinguishes the vacuum from a table is that it looks the same to every observer whatever their orientation or velocity — not that its energy density vanishes.Section 1.2, Eq. 1.6
Settled physics02Vacuum energy is not a modelling assumption that could be dropped. Bousso writes that we know vacuum energy exists in nature, because we can manipulate the amount of vacuum energy in bounded regions in Casimir-type experiments; and that even if the constant were unobservably small today, the Standard Model would still say it was large and positive in the early universe before electroweak symmetry breaking.Section 2.2, the paragraphs answering the notion that vacuum energy is optional
Settled physics03The known contributions overshoot the measured value by 60 to 120 orders of magnitude. Electron loops trusted only to 100 GeV give about ten to the minus sixty-eighth in Planck units, a supersymmetry-breaking cutoff near one TeV gives at least ten to the minus sixty-fourth, and a Planck-scale cutoff gives order unity, against an empirical bound on the total vacuum energy of about ten to the minus one hundred and twenty-first.Section 1.2, Eqs. 1.5 and 1.9; the summary of the discrepancy at the end of Section 1.2
What to watch04Dark energy is vacuum energy. The value determined from supernovae and refined by the seven-year microwave-background data with baryon acoustic oscillations and the Hubble constant is 1.35 plus or minus 0.15 times ten to the minus one hundred and twenty-third in Planck units; quintessence and large-distance modifications of general relativity add tuned parameters, are less predictive, and leave the cosmological constant problem exactly where it was.Section 2.1, Eq. 2.1; Section 2.2
Published and peer-reviewed05The speculative half: string theory compactified from nine spatial dimensions may have of order ten to the five hundredth distinct three-dimensional vacua, giving a spectrum of the constant so dense that roughly ten to the three hundred and seventy-seventh of them sit below the observed value, and eternal inflation produces every one of them dynamically as widely separated bubble regions from generic initial conditions.Sections 3.1 to 3.5, Figs. 2 and 3
What to watch06The framework yields a number to check against. Applying the causal patch measure to the landscape predicts that observers who live a time after their bubble forms will find a cosmological constant of order the inverse square of that time; with an age of about 13.7 billion years the prediction matches the measured value, and it addresses the coincidence problem as well, independently of any assumption about what observers are made of.Section 3.7, Eq. 3.3 and Fig. 4
What to watch
Read it · abstract
Abstract
In this colloquium-level account, I describe the cosmological constant problem: why is the energy of empty space at least 60 orders of magnitude smaller than several known contributions to it from the Standard Model of particle physics? I explain why the "dark energy" responsible for the accelerated expansion of the universe is almost certainly vacuum energy. The second half of the paper explores a more speculative subject. The vacuum landscape of string theory leads to a multiverse in which many different three-dimensional vacua coexist, albeit in widely separated regions. This can explain both the smallness of the observed vacuum energy and the coincidence that its magnitude is comparable to the present matter density.
(Abstract only — see the rights note above. The full text is free to read at arXiv:1203.0307. The companion cosmological-constant sheets in this library are Steven Weinberg’s 1989 review at /library/stm-5610822bc8 and Jérôme Martin’s 2012 account at /library/stm-568da33759.)
The way in
https://arxiv.org/abs/1203.0307LICENCE. The manuscript is arXiv:1203.0307, posted 1 March 2012 and revised 5 March 2012, and the arXiv record carries the arXiv.org perpetual non-exclusive distribution licence version 1.0 — checked on the arXiv abstract page on 2026-09-08 — which is not a Creative Commons licence and does not grant redistribution. No Creative Commons statement appears in the text. So this page carries the summary, the claims and the author’s own abstract, and sends the reader to the source. The paper is a colloquium-level account, based on colloquia given at Caltech, MIT and the University of Michigan at Ann Arbor and on a lecture at Subnuclear Physics: Past, Present and Future, Pontifical Academy of Sciences, Vatican, October 2011, and it is marked prepared for submission to JHEP. Bousso writes from the Center for Theoretical Physics and Department of Physics, University of California, Berkeley, and Lawrence Berkeley National Laboratory. Section, equation and figure numbers in the claims below are those of the arXiv v2 manuscript.
How to cite it
Raphael Bousso (2012) The Cosmological Constant Problem, Dark Energy, and the Landscape of String Theory. arXiv:1203.0307
Where it sits in the curriculum