^{3}.

We study the backreaction of superhorizon fluctuations of a light quantum scalar field on a classical de Sitter geometry by means of the Wilsonian renormalization group. This allows us to treat the gravitationally amplified fluctuations in a nonperturbative manner and to analytically follow the induced renormalization flow of the spacetime curvature as long wavelength modes are progressively integrated out. Unbounded loop corrections in the deep infrared are eventually screened by nonperturbative effects which stabilize the geometry.

Despite more than half a century of effort (and substantial progress), the extreme smallness of the measured cosmological constant in Planck units remains a major open issue in physics, which directly questions our fundamental understanding of gravity

Fortunately, a complete theory of quantum gravity might not be needed to address this question, which concerns the far infrared sector of the theory

The route to establish this scenario is, however, paved with serious technical difficulties. Leave alone the hard task of properly computing graviton loop corrections in a de Sitter geometry

Here, we propose a novel perspective on the problem of backreaction based on the recent developments of nonperturbative renormalization group (NPRG) techniques in de Sitter spacetime

This approach offers various technical advantages. First, of course, we fully capture the nonperturbative character of the problem. Second, we can consistently work in de Sitter spacetime since we follow the RG trajectory of the theory, instead of its time evolution. Third, we can focus specifically on the role of the infrared modes, the ultraviolet contributions being absorbed in the initial conditions of the RG flow. Finally, as we shall see below, most calculations can be performed analytically thanks to the simple nature of the RG flow in the far infrared.

We consider the theory of a quantum scalar field

The second equation in Eq.

The physics of the massless, minimally coupled scalar field in de Sitter spacetime is well known: Fluctuations on superhorizon scales are dramatically amplified by the gravitational field, which results in nonperturbative infrared effects. In the NPRG framework, this is manifest in the phenomenon of dimensional reduction

An important consequence is that the functional integral representation of the infrared effective theory reduces to a simple integration over the single fluctuating degree of freedom left

Using the representation

We can further simplify this equation by using the identity

The exact flow of

Deviations from the solution

Flow of the spacetime curvature

However, when the one-loop correction becomes significant, higher orders also become important and, in fact, the perturbative expansion breaks down, as also illustrated in Fig.

The complete flow is obtained by solving Eq.

In conclusion, we have investigated the backreaction of a light quantum scalar field on a de Sitter geometry by means of recently developed NPRG techniques. We find a nontrivial renormalization of the spacetime curvature as superhorizon fluctutations are progressively integrated out. Perturbative loop corrections grow unbounded as a result of the gravitational amplification of such fluctuations. This signals the breakdown of perturbation theory rather than an instability. Nonperturbative effects come into play with, in particular, the dynamical generation of a mass, which screens the growth of superhorizon fluctuations and freezes the RG flow of the effective spacetime curvature. Overall, the infrared renormalization of the latter is controlled by the gravitational coupling

We believe the present work brings an interesting light on the general issue of de Sitter spacetime stability against quantum fluctuations. It is worth emphasizing, though, that here we have discussed the specific case of superhorizon fluctuations of a quantum scalar field in a de Sitter invariant quantum state. Various other possible sources or directions of instability have been discussed in the literature such as, for instance, the question of stability of a global de Sitter geometry (as opposed to the expanding Poincaré patch studied here)

Were we to speculate about these questions from the present work, we would expect that the physical mechanism studied here, namely, the saturation of the flow due to the phenomenon of dynamical mass generation, is likely to be at work for scalar fields even in a non–de Sitter invariant state. However, no such phenomenon is expected for graviton fluctuations. The fate of the latter beyond perturbation theory and the question of a possible saturation mechanisms in that case are left open.