We study the backreaction of superhorizon fluctuations of a light quantum scalar field on a classical de Sitter geometry by means of the Wilsonian renormalisation group. This allows us to treat the gravitationally amplified fluctuations in a nonperturbative manner and to analytically follow the induced renormalisation 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 stabilise the geometry.Despite more than half a century of efforts (and numerous progresses), 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 [1][2][3]. In the language of quantum field theory, the problem appears as that of an unnatural fine tuning between the-a priori arbitrary-bare cosmological constant, allowed by all symmetries known to date, and the-inevitably largequantum contribution from vacuum fluctuations of the Standard Model fields. Some potential key players are, however, missing in this picture. Obvious ones are the quantum fluctuations of the gravitational field itself, which have been suggested early on as a possible solution of the puzzle [4][5][6]. There coud also be important backreaction effects of the quantum fluctuations in the matter (nongravitational) sector [7][8][9][10][11].Fortunately, a complete theory of quantum gravity might not be needed to address this question, which concerns the far infrared sector of the theory [6]. A semiclassical description, with quantum fluctuations selfconsistently coupled to a (dynamical) classical gravitational field through Einstein's equations, already provides a framework for a possible solution. In the absence of quantum fluctuations, the classical solution to Einstein's equations with a positive (negative) cosmological constant is the maximally symmetric de Sitter (anti-de Sitter) geometry. In this context, it has been long suggested that the classical de Sitter geometry may be unstable against quantum fluctuations [4-6, 8-11], a possibility which has received a renewed interest in the past two decades [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. In standard cosmological coordinates, the qualitative picture goes as follows. The accelerated spacetime expansion pulls appart particleantiparticle pairs from the quantum vacuum. The selfgravitation of the latter may then slows the expansion down, resulting in an effective decay of the spacetime curvature, that is, of the effective cosmological constant.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 [28][29][30], even the case of a simple scalar quantum field is far from trivial. First, con-vincingly assessing the question of a possible instability (beyond a linear analysis) requires one to actually control ...