STM-D-0663Paper2013What to watch

The Cosmological Constant Problem: Why it's hard to get Dark Energy from Micro-physics

C. P. Burgess

Abstract and summary · read the original at the source

In one page

Cliff Burgess wrote these Les Houches lectures to state, as precisely as anyone has, why the vacuum’s energy is the hardest open question in physics. His argument runs in three moves. First, Lorentz invariance decides how a vacuum energy must gravitate: pressure equal to minus the energy density, exactly the behaviour dark energy shows. Second, the famous headline number — theory beating observation by 10¹²² — is, he says, a straw man, because the cutoff it depends on cancels out of any real prediction. Third, the honest version is worse in a more interesting way: once everything is written in measured masses, the electron alone contributes about 10³⁰ times too much vacuum energy, and the Z boson about 10⁵⁴. That is the gap to explain. Burgess sets three tests any solution must pass, backs two supersymmetric large extra dimensions as the most promising route, and closes that the problem is a message of hope: new physics must be close.

Why it matters hereChapter 2 rests on the vacuum having a real and enormous energy density, and this is the clearest published statement of what that costs us: the mismatch is not an artefact of a cutoff, it is there in the electron. Chapter 13 needs exactly this, because any unified picture in which zero-point energy and dark energy are one quantity has to say what happens to the other fifty orders of magnitude — and Burgess supplies the criteria to judge an answer by, plus a route that gets tested by benchtop gravity at micron distances rather than by argument.

What it claims

01Lorentz invariance settles how a vacuum energy would gravitate. The only stress-energy tensor consistent with an invariant vacuum is proportional to the inverse metric, conservation of that tensor then forces the energy density to be a constant, and comparing with a perfect fluid gives a pressure equal to minus the energy density — an equation-of-state parameter of exactly minus one, which is what the dark-energy observations show.Section 1.1, Eqs. 1.1 to 1.3
Settled physics
02The famous headline mismatch — cut the mode sum off at the Planck mass and the predicted vacuum energy exceeds the observed value by a factor of about 10¹²² — is described by Burgess as something of a straw man. The cutoff is an artificial scale introduced to regulate integrals, and in every other part of quantum field theory that dependence is absorbed by renormalisation of the parameters of the Lagrangian; tracking ultraviolet divergences is therefore misleading when asking whether a theory is natural.Section 1.3, Eqs. 1.21 to 1.23; Section 3, point 3
Published and peer-reviewed
03The sharper version of the problem survives renormalisation and is stated in measured quantities. Each particle species contributes a term of order its mass to the fourth power divided by sixteen pi squared, independent of any cutoff. The electron alone overshoots the observed dark-energy density by about 10³⁰, and the Z boson by about 10⁵⁴ — so the honest size of the discrepancy is of order 10⁵⁰, and it is carried by the particle we understand best.Section 1.3, Eqs. 1.24 and 1.25
Published and peer-reviewed
04Technical naturalness is the criterion Burgess proposes, and it asks two separate questions of any small parameter: why it is small in the underlying microscopic theory, and why it stays small as the higher-energy modes are integrated out to give the effective theory at the scale where it is measured. For the cosmological constant, matching the sub-eV value requires the constant in the effective theory above the electron mass and the electron’s own quantum correction to cancel to better than thirty decimal places, and every other well-understood hierarchy of scale between cosmology and particle physics does have a technically natural explanation.Section 1.4, Eq. 1.28; Section 3, point 1
Published and peer-reviewed
05Three minimal criteria are set for any candidate solution: it must work beyond the classical approximation, since there is no problem at all classically; it must apply at scales above an electronvolt, since that is where the quantum problem starts; and it must do no harm to the physics already established at those scales. The rule of thumb Burgess gives is to ask whether a proposal can include the electron, and his assessment of the field in 2013 is that none of the popular models satisfies all three.Section 1.5; Section 3, point 4
Published and peer-reviewed
06His own preferred direction is two supersymmetric large extra dimensions, because extra dimensions break the direct link between a four-dimensional Lorentz-invariant vacuum energy and a large four-dimensional curvature, and supersymmetry in the bulk combines scale invariance with supersymmetry in a way that evades Weinberg’s no-go result. What to watch: the picture is falsifiable at the bench. It requires Newton’s inverse-square law to cross over to an inverse fourth power at distances tied to the dark-energy density — of order a micron, with the longest Kaluza-Klein wavelength near 0.9 micron for extra dimensions of about 1.3 micron — no superpartners at the LHC, and energy loss into the extra dimensions if the higher-dimensional Planck scale is near 10 TeV. Burgess’s closing verdict is that the cosmological constant problem is a message of hope, not despair: by being large, the Universe is telling us that new physics is just around the corner.Section 2.2, Opportunities and worries; Section 3, point 5
What to watch

Read it · abstract

Abstract

These notes present a brief introduction to naturalness' problems in cosmology, and to the Cosmological Constant Problem in particular. The main focus is the old' cosmological constant problem, though the more recent variants are also briefly discussed. Several notions of naturalness are defined, including the closely related ideas of technical naturalness and `t Hooft naturalness, and it is shown why these naturally arise when cosmology is embedded within a framework --- effective field theories --- that efficiently captures what is consistent with what is known about the physics of smaller distances. Some care is taken to clarify conceptual issues, such as the relevance or not of quadratic divergences, about which some confusion has arisen over the years. A set of minimal criteria are formulated against which proposed solutions to the problem can be judged, and a brief overview made of the general limitations of most of the approaches. A somewhat more in-depth discussion is provided of what I view as the most promising approach. These notes are aimed at graduate students with a basic working knowledge of quantum field theory and cosmology, but with no detailed knowledge of particle physics.

The way in

https://arxiv.org/abs/1309.4133Lectures given by Cliff Burgess of McMaster University and the Perimeter Institute for Theoretical Physics to the Les Houches Summer School ’Post-Planck Cosmology’, 8 July to 2 August 2013, and posted to arXiv on 16 September 2013 as arXiv:1309.4133, 52 pages, marked by the author as a preliminary draft. The arXiv abstract page carries the arXiv.org perpetual non-exclusive distribution licence rather than a Creative Commons licence, and no CC statement appears in the text, so this sheet carries the summary, the claims and the author’s own abstract; the complete lectures are free to read at arxiv.org/abs/1309.4133. The research was supported in part by the Natural Sciences and Engineering Research Council of Canada, and research at the Perimeter Institute by the Government of Canada and the Province of Ontario.

How to cite it

C. P. Burgess (2013) The Cosmological Constant Problem: Why it's hard to get Dark Energy from Micro-physics. arXiv:1309.4133

Where it sits in the curriculum

What the vacuum is Inertia and gravity from the vacuum The unified picture