nLab Witten's Dark Fantasy



String theory




What has been called Witten’s Dark Fantasy (in Heckmann-Lawrie-Lin-Zoccarato 19, Section 8) is an argument, going back to Witten 95a, Witten 95b, Sec. 3, Witten 00, p. 7, for the existence of non-perturbative non-supersymmetric 4d string vacua/string phenomenology with fundamentally vanishing cosmological constant (i.e. vanishing “dark energy”).

The original idea was formulated in terms of 3d M-theory on 8-manifolds decompactified at strong coupling to 4d via duality between M-theory and type IIA string theory (recall the super 2-brane in 4d).

Based on an observation of Vafa 96, Section 4.3 that the argument should have a natural realization in 4d F-theory on Spin(7)-manifolds (T-dual to the previous perspective), a detailed construction was finally laid out in Bonetti-Grimm-Pugh 13, Heckmann-Lawrie-Lin-Zoccarato1 18, Heckman-Lawrie-Lin-Sakstein-Zoccarato 19.



The key technical point is the claim that a careful analysis of D=4 N=1 supergravity obtained after KK-compactification of F-theory on Spin(7)-manifolds (T-dual to M-theory on Spin(7)-manifolds) reveals, in contrast to the N=1 supersymmetry of F-theory on CY4-folds, an “N=1/2N= 1/2 supersymmetry”, where:

  1. the vacuum state is supersymmetric and hence has vanishing cosmological constant;

  2. but no finite-energy-excitation of the vacuum appears supersymmetrically,

    hence fermions and bosons in the model do not appear in supersymmetric spectra.

(Vafa 96, Sec. 4.3 BGP 13, HLLZ 18, Sec. 4)

Closed spatial slices

The concrete realization of Witten's Dark Fantasy in the F-theory model of Heckmann-Lawrie-Lin-Zoccarato1 18 is a cosmology where spatial slices are closed and in fact of the topology of the 3-sphere:

graphics from Heckman-Lawrie-Lin-Sakstein-Zoccarato 19


When the idea of “Witten’s Dark Fantasy” was proposed in Witten 95a, Witten 95b, Witten 00 it was right before observation of red shifts of supernovae convinced cosmologists, in 2001, of a relatively small but positive cosmological constant. When this result became enshrined in what is now the standard model of cosmology, the idea of vanishing cosmological constant in string theory fell out of favor, and a vocal sub-community instead embarked on arguing that de Sitter spacetime-string vacua with positive cosmological constant had to be searched at random in a large landscape of string theory vacua.

However, debate remains over whether the apparently observed cosmological constant is actually real:

  1. The authors of KLKCR 19 claim that temporal evolution of supernovae luminosity had been underappreciated, which makes the apparent evidence for a positive cosmological constant completely go away. Earlier, NGS 16 had pointed out that even with the established interpretation of the data, a vanishing cosmological constant is not excluded by the data.

  2. Since around 2000 authors have argued that the apparent cosmological constant may be an artifact of the usual FRW model-cosmologies not taking sizeable backreaction of cosmic inhomogeneities into account. The situation with this debate currently remains open (see at inhomogeneous cosmology).

    While it is uncontroversial that cosmic inhomogeneity does have a measurable effect on cosmic expansion, the general current consensus seems to be that it is too small to explain all of the dark energy of the standard model of cosmology. But in view of the first item above, this would be a moot point.

from KLKCR 19

In the extreme case, if re-analysis of the data, combined with effects of cosmic inhomogeneity, and possibly combined with higher curvature corrections to gravity (such as control the observationally preferred Starobinsky model of cosmic inflation), would explain all of the apparently observed cosmological constant, then Witten’s dark fantasy would again appear to be viable string phenomenology.

It is then interesting to notice that also the closed spatial slices found in the model above have recently been argued to be preferred by observational data (VMS 19).

That available experimental data supports neither a cosmological constant nor open spatial slices is further argued in Di Valentino-Melchiorri-Silk 20.



General idea

The idea in rough form goes back to

The observation that the idea should naturally embed in F-theory, namely as F-theory on Spin(7)-manifolds is due to

Detailed implementation

A detailed implementation of the idea in F-theory on Spin(7)-manifolds is developed in:


The standard model of cosmology, as per 2020, with its positive dark energy-density and open spatial slices contradicts the vanishing cosmological constant and preferred closed (spherical) spatial slices of Witten's Dark Fantasy.

It may very well be that Witten's Dark Fantasy is phenomenologicaly unviable. But it is interesting to notice that there is recent and very recent astrophysical analysis which claims problems with exactly these two aspects of the standard model of cosmology. If these contrarian authors are actually right, then Witten's Dark Fantasy is exactly the kind of model needed to match observation.

Dark energy or not?

Argument that the observed type Ia supernovae are actually consistent with a vanishing cosmological constant:

Stronger argument that the observed type Ia supernovae in fact prefer a vanishing cosmological constant (due to time-dependency of SN brightness that had been missed):

Open spatial slices or not?

Arguments that the PLANCK satellite data actually prefers a closed spatial slices (contrary to the assumption in the current standard model of cosmology):

A critique of these arguments is given in

  • George Efstathiou, Steven Gratton, The evidence for a spatially flat Universe (arXiv:2002.06892)

but this critique again rests on just the combination Planck collaboration & baryon acoustic peak (BAO) & supernova-data which the above references argue cannot sensibly be combined.

From the abstract of Handley 19:

The curvature parameter tension between Planck 2018, cosmic microwave background lensing, and baryon acoustic oscillation data is measured using the suspiciousness statistic to be 2.5 to 3σ. Conclusions regarding the spatial curvature of the universe which stem from the combination of these data should therefore be viewed with suspicion. Without CMB lensing or BAO, Planck 2018 has a moderate preference for closed universes, with Bayesian betting odds of over 50:1 against a flat universe, and over 2000:1 against an open universe.

Both or neither?

Combined argument that experimental data disfavours both a cosmological constant (favoring instead effective phantom dark energy) as well as an open universe:

  • Eleonora Di Valentino, Alessandro Melchiorri, Joseph Silk, Cosmic Discordance: Planck and luminosity distance data exclude LCDM (arXiv:2003.04935)

Last revised on July 21, 2022 at 08:36:23. See the history of this page for a list of all contributions to it.