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 the 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 many authors have argued that the apparent cosmological constant may be an artefact 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).



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

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-desity 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 exavtly 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:

  • J. T. Nielsen, A. Guffanti & Subir Sarkar, Marginal evidence for cosmic acceleration from Type Ia supernovae, Nature Scientific Reports volume 6, Article number: 35596 (2016) (arXiv:1506.01354, web discussion)

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?

Argument that the PLANCK satellite data prefers a closed spatial slices:

  • Eleonora Di Valentino, Alessandro Melchiorri, Joseph Silk, Planck evidence for a closed Universe and a possible crisis for cosmology, Nature Astronomy 2019 (doi:1911.02087) doi:s41550-019-0906-9

Last revised on January 9, 2020 at 12:38:54. See the history of this page for a list of all contributions to it.