# Is dark energy really a mystery?

Eugenio Bianchi, Carlo Rovelli, Rocky Kolb

► To cite this version:

Eugenio Bianchi, Carlo Rovelli, Rocky Kolb. Is dark energy really a mystery?. Nature, 2010, 466 (7304), pp.321. 10.1038/466321a. hal-01258351

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# Is dark energy really a mystery?

The Universe is expanding. And the expansion seems to be speeding up. To account for that acceleration, a mysterious factor, 'dark energy', is often invoked. A contrary opinion — that this factor isn't at all mysterious — is here given voice, along with counter-arguments against that view.

<figure><img src="image_2.png" /><figcaption>Figure 1 | Cosmic expansion. As the Universe expands, space stretches much like the surface of an inflating balloon, and galaxies get farther and farther apart. Data indicate that the rate of this expansion is accelerating.</figcaption></figure>

## No it isn't — Eugenio Bianchi and Carlo Rovelli

Is cosmic acceleration¹ such a great problem? Many commentators have argued that it is, and that the explanation is to be found in invoking a mysterious substance, dark energy, that as yet has no theoretical underpinning²,³.

We disagree. An explanation is to hand and has been for many years. Cosmic acceleration is predicted and simply described by the theory of general relativity, together with a non-vanishing cosmological constant, $Λ$. Our case, presented here in summary, is made in detail in a paper⁴ posted on the arXiv preprint server.

The $Λ$ cold dark matter ($Λ$CDM) cosmological model assumes the presence of $Λ$ and is "almost universally accepted by cosmologists as the best description of the present data"⁵. Three objections to $Λ$ are commonly presented, and nourish the 'mystery'. We argue that there is confusion — historical or conceptual — in each of them.

The first objection is known as 'Einstein's blunder'. Allegedly, $Λ$ was rejected by general relativists, and indeed by Einstein himself, who first considered it but later called it his "greatest blunder". But Einstein's 'blunder' was not $Λ$. It was failing to see that — with or without $Λ$ — the Universe isn't static in his theory of general relativity, thereby missing an easy prediction of the cosmic expansion (Fig. 1) before its discovery. $Λ$ is not an appendage to Einstein's theory added to account for observations: it is an integral and natural part of it. Its nature and scale are no more or less mysterious than any of the several other constants in our fundamental theories.

The second objection is termed the 'coincidence problem'. Data indicate that we happen to live in a 'short' phase of cosmic history, during which the contributions from matter and $Λ$ to the
cosmic dynamics are comparable in magnitude. Such an 'unlikely coincidence' is presented as an argument against the ΛCDM hypothesis. But if the ratio of these contributions as a function of cosmic time is properly considered on a linear rather than a logarithmic scale, it can be seen that such a 'short' phase lasts for half the life of the Universe, and there is no 'unlikely' coincidence. In any case, we should not assume that we live in a fully random place or time in the Universe, as the coincidence-problem objection presupposes. The density around us, for instance, is very far from the average cosmic density.

The third objection concerns ‘vacuum energy’. Quantum field theory (QFT) seems to predict a vacuum energy that adds to the cosmological force due to Λ — just as radiative corrections affect the charge of the electron. But this hypothetical contribution to Λ is much larger than the observed Λ. The discrepancy is an open puzzle in QFT in the presence of gravity⁶,⁷. But it is a conceptual mistake to confuse Λ with QFT’s vacuum energy. Λ cannot be reduced to the ill-understood effect of QFT’s vacuum energy — or that of any other mysterious substance. Λ is a sort of ‘zero-point curvature’; it is a repulsive force caused by the intrinsic dynamics of space-time.

Tests on the ΛCDM model must continue and alternative ideas must be explored. But it is our opinion — and that of many relativists — that saying dark energy is a ‘great mystery’, for a force explained by current theory, is misleading. It is especially wrong to talk about a ‘substance’. It is like attributing the force that pushes us out of a turning merry-go-round to a ‘mysterious substance’.

Eugenio Bianchi and Carlo Rovelli are at the Centre de Physique Théorique de Luminy, Case 907, Luminy, Marseille F-13288, France. e-mails: rovelli@cpt.univ-mrs.fr; bianchi@cpt.univ-mrs.fr

**Yes it is — Rocky Kolb**

The ΛCDM is the most complete, predictive and successful cosmological model ever devised, capable of accounting for an enormous number of astronomical observations. At present, there are no observations discrepant with the ΛCDM model.

But the success of ΛCDM comes at a price. In the model, only about 5% of the total mass-energy of the Universe is observed and understood, and 95% of the Universe is dark. The dark side includes 25% of the total mass-energy in the form of dark matter binding together galaxies and other large-scale structures, and 70% in the form of dark energy driving galaxies apart in an accelerating cosmic expansion.

Cosmologists usually refer to dark matter and dark energy as cosmic mysteries. Bianchi and Rovelli⁴ argue that dark energy can be explained by invoking a new constant of nature, a cosmological constant. They assert that this is a simple, acceptable, non-mysterious explanation for dark energy. I disagree. In my opinion, a cosmological constant qualifies as a mystery in the non-theological sense of the word⁸: “Something not understood or beyond understanding.”

Einstein's cosmological constant $\Lambda$ is the simplest explanation for dark energy: it adequately fits the data, and there is no reason to exclude it. But the magnitude of $\Lambda$ necessary to explain the observations places it far “beyond [our] understanding”.

If the cosmological constant is the explanation for dark energy, $\Lambda$ must be about $(10^{28} \text{ cm})^{-2}$. The length $10^{28} \text{ cm}$ is absurdly large, and cannot at present be related to any other known or expected length scale in nature. Attempts to explain this new length scale fail by many, many orders of magnitude.

We must demand more of cosmology than just piling on components or constants to a model to reproduce observations. Otherwise, we would still happily be adding epicycles to the Ptolemaic model of planetary motion. Cosmological models, along with their constants and components, must be grounded in laws of nature that we understand. The magnitude of the
cosmological constant cannot currently be explained by any physics we know. Until it is, it is a
mystery.

Recalling the warning of astrophysicist Tommy Gold (personal communication), "for every complicated physical phenomenon there is a simple, wrong explanation", it would be a mistake to be satisfied with the cosmological constant just because it is a simple explanation.

Rocky Kolb is in the Department of Astronomy and Astrophysics, University of Chicago, Chicago, Illinois 60637, USA. e-mail: rocky.kolb@uchicago.edu

1. Carroll, S. M. Living Rev. Rel. 4, 1–56 (2001).

2. Calder, L. & Lahav, O. Phys. World 23 (June), 32–37 (2010).

3. Tyson, J. A. Nature 464, 172–173 (2010).

4. Bianchi, E. & Rovelli, C. Preprint at http://arxiv.org/abs/1002.3966 (2010).

5. Lahav, O. & Liddle, A. R. Preprint at http://arxiv.org/abs/1002.3488 (2010).

6. Wald, R. M. Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics (Univ. Chicago Press, 1994).

7. Rovelli, C. Quantum Gravity (Cambridge Univ. Press, 2004).

8. www.merriam-webster.com/dictionary/mystery