What do we really know about Dark Energy?
Ruth Durrer
Abstract and summary · read the original at the source
In one page
Ruth Durrer, a cosmologist at Geneva, takes the biggest number in the universe and asks how it was actually measured. Her answer is that it was not — not directly. Supernovae, the microwave background and baryon acoustic oscillations all agree, and what they all agree on is one thing: the distance out to a given redshift is bigger than a matter-only universe with the Hubble rate we measure locally would give. Everything else is inference, made by feeding that distance into a formula that only holds if the universe is exactly smooth. Along the way she makes the point this site is built on and makes it flatly: a cosmological constant and a vacuum energy density are the same object under two names — same form, same coupling, no experiment can ever tell them apart — so we should stop pretending they are different. Cosmology then measures the vacuum. Then she names the observations that would settle the rest.
Why it matters hereChapter 2 has no better citation for its central identification: Durrer states outright that a cosmological constant is in no way distinguishable from vacuum energy, that no experiment can ever separate them, and that cosmology therefore measures the present vacuum energy density — while a footnote reminds the reader that differences of vacuum energy are measured all the time, in the Casimir force and the Lamb shift. Chapter 13 gets the same join from the cosmological side, and the famous mismatch between the measured value and the value a quantum field theory estimate returns. Chapter 1 gets a working example of the evidence ladder, because Durrer separates the measurement from the interpretation line by line and names the observation that would settle it.
What it claims
01A cosmological constant is in no way distinguishable from vacuum energy: both take the form of the metric multiplied by an energy density, and both couple only to gravity, so no experiment can ever tell them apart. Durrer’s conclusion is that the two should not be distinguished, and cosmology then determines the present vacuum energy density to be about 2.7 thousandths of an electronvolt, raised to the fourth power, times the square of the reduced Hubble parameter.Sec. 1, Introduction, numbered point 2
Settled physics02Differences of vacuum energy are very well measurable — the Casimir force and the Lamb shift in atomic spectra are the examples Durrer gives — even though the absolute level is not.Sec. 1, Introduction, footnote 1
Settled physics03Estimating the vacuum energy from particle physics gives the wrong answer by 60 orders of magnitude if the supersymmetry-breaking scale sets it, and by 120 orders of magnitude if the string or Planck scale does — in Durrer’s words probably the worst estimate ever in physics. A counter term does not repair it, because vacuum energy is not protected in quantum theory: corrections run like the fourth power of the cutoff and must be readjusted at every order in perturbation theory.Sec. 1, Introduction, numbered point 2
What to watch04Many independent probes with different systematics converge on the same result — a matter density parameter times the square of the reduced Hubble parameter of about 0.13, and a distance at redshift around one that a flat matter-dominated universe cannot produce. Supernovae give a luminosity distance, baryon acoustic oscillations and the microwave background give an angular diameter distance to last scattering at redshift about 1090.Sec. 2, What do we really measure, subsections 2.1 to 2.6; Sec. 3, first paragraph
Settled physics05No cosmological probe measures the cosmological constant, or the dark energy density, or its equation of state. Each infers them from the distance-redshift relation by assuming the Friedmann-Lemaitre formula for that relation, which holds only in an exactly homogeneous and isotropic universe — and the real universe is at least perturbed, with curvature perturbations on galactic scales far larger than the background term.Sec. 3, What do we know about dark energy; Sec. 4, Conclusions, first paragraph
Published and peer-reviewed06The assumption is testable, and Durrer names how. In a Friedmann-Lemaitre universe the expansion rate at a redshift and the distance to that redshift are locked together by one formula; measuring both independently checks whether the formula holds for the real universe. Good distances reach redshift about 0.5, independent expansion rates do not yet exist, and large galaxy surveys such as the Dark Energy Survey and Euclid should supply them by measuring the radial and the transverse matter power spectrum separately. A second test is the growth factor of linear perturbations, from weak lensing or from correlating large-scale structure with the integrated Sachs-Wolfe effect, because a universe dominated by a cosmological constant modifies that growth in a specific way that a misread distance would not mimic.Sec. 3, final two paragraphs; Sec. 4, Conclusions
What to watch
Read it · abstract
Abstract
In this paper I discuss what we truly know about dark energy. I shall argue that up to date our single indication for the existence of dark energy comes from distance measurements and their relation to redshift. Supernovae, CMB anisotropies and observations of baryon acoustic oscillations, they all simply tell us that the observed distance to a given redshift is larger than the one expected from a Friedmann Lemaitre universe with matter only and the locally measured Hubble parameter.
The way in
https://arxiv.org/abs/1103.5331LICENCE. The arXiv posting 1103.5331, version 3 of 25 September 2011, carries the arXiv non-exclusive distribution licence version 1.0 — arXiv distribution rights only, no re-use — checked on the arXiv abstract page on 2026-09-08, and no Creative Commons statement appears in the manuscript text. So this sheet carries the summary, the claims and the author’s own abstract and sends the reader to the full text at the source. CITATION. This is Durrer’s invited talk at the Royal Society meeting Cosmological Tests of General Relativity, organised by Rachel Bean, Pedro Ferreira and Andy Taylor, and it was published as Philosophical Transactions of the Royal Society A 369, number 1957, pages 5102 to 5114 (2011), doi 10.1098/rsta.2011.0285; the arXiv version 3 is the one in print. Durrer wrote from the Institut de Physique Théorique at CEA and CNRS, Gif-sur-Yvette, and from the Département de Physique Théorique at the Université de Genève. TEXT. The claims below are read from the complete arXiv manuscript and the locators use its own section, equation and footnote numbering.
How to cite it
Ruth Durrer (2011) What do we really know about Dark Energy?. arXiv:1103.5331
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