Quote Of The Day

[B]eware that there are general arguments in quantum gravity, independent of string theory, that global de Sitter spacetime is inconsistent, see e.g. Rajaraman 16 and references given there. If true, this means that no quantum consistent model for observed cosmology will be totally straightforward, all of them will have to realize a de Sitter cosmology as an effective phenomenon on the backdrop of non-de Sitter cosmology.

From Urs Schreiber at the Physics Forums.

The paper referenced is:

Graviton loop corrections to observables in de Sitter space often lead to infrared divergences. We show that these infrared divergences are resolved by the spontaneous breaking of de Sitter invariance.

Arvind Rajaraman, "de Sitter Space is Unstable in Quantum Gravity" (Submitted on 25 Aug 2016 (v1), last revised 17 Sep 2016 (this version, v2)).

The conclusion of the paper states:

We have argued that de Sitter space is not a solution to gravity coupled to a cosmological constant when quantum effects are taken into account. The classical equations of motion receive quantum corrections which are singular if the solution is taken to be de Sitter. We have argued that the deviations from de Sitter are calculable, and that the true solution is deformed away from de Sitter by a parameter proportional to √ κ. 

The argument for this was straightforward. In the exact metric of de Sitter space, there are gravitational perturbations whose propagator is ill defined, and which caused infrared divergences. A small deviation from de Sitter parametrized by a small parameter ǫ allows these modes to have a well defined propagator. However, the quantum effective action computed around this new metric now generically has terms which go as 1 ǫ . The quantum equations of motion are singular as we take ǫ to zero, and cause de Sitter to not be a solution when quantum corrections are included. (Another way to say this is that the de Sitter metric has an infinite action when quantum effects are included.) The calculation in the previous section argues that these qualitative arguments can be made quantitative, and that the perturbation away from de Sitter can be computed in perturbation theory. 

These arguments are related to previous arguments in the literature, for instance by Polyakov. While Polyakov has argued that scalar field theory in de Sitter (using the in-out formalism) already leads to an instability, we have shown that gravitons produce an instability in the more controlled in-in formalism. The in-in formalism is expected to asymptote to the in-out result when the intermediate time is taken to infinity; it would be interesting to see if this is the case. 

The Schwinger-Keldysh propagator for the gravitational perturbations is enhanced by a factor proportional to √ 1 κ . This indicates that the gravitational perturbation series, which is normally in powers of κ, is modified. A 1-loop diagram with a Schwinger-Keldysh propagator now scales as √ κ and in general, the perturbation series becomes an expansion in √ κ. 

We should also discuss the occasionally thorny issue of gauge invariance. It is well known that tadpoles of gravitons are not gauge invariant, and so one might wonder about the stautus of the tadpoles we have calculated. The resolution is that our intermediate steps have been performed in a fixed gauge, but our final result (that de Sitter is unstable) is a gauge invariant statement. It is therefore valid in any gauge. Similarly, the deformed metric is not a gauge invariant quantity, but it has been presented in a particular gauge, and can be transformed to any gauge of choice. 

A more subtle issue is the question of observables in quantum gravity. It is often argued that correlation functions, even for a fixed geodesic distance, are not well defined; this is roughly because any pointlike sources are smeared into black holes. However, our corrections are of order √ κ and therefore scale faster than any perturbative effect in quantum gravity, including the size of black holes. They are hence dominant at weak coupling and will not be washed out by quantum gravity effects. 

Finally we note that this solution to the issue of the IR divergences may potentially lead to observable effects, at least if the Hubble scale is large enough. We leave this issue for future work.