Historical research guide · 0729 · 2012
The Cosmological Constant Problem, Dark Energy, and the Landscape of String Theory
Raphael Bousso
In one minute
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.
Connection
Chapter 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.
From the source
The 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
Vacuum 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
The 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
Dark 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
The 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
The 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
The way in
https://arxiv.org/abs/1203.0307How to cite it
Raphael Bousso (2012) The Cosmological Constant Problem, Dark Energy, and the Landscape of String Theory arXiv:1203.0307