  We study the backreaction of gravitationally amplified quantum fluctuations
of scalar fields on a classical de Sitter geometry. We formulate the problem in
the framework of the Wilsonian renormalisation group, which allows us to treat
the scalar field fluctuations in a nonperturbative manner and to follow the
renormalisation flow of the spacetime curvature as long wavelength,
superhorizon fluctuations are progressively integrated out. For light fields in
units of the spacetime curvature, these are described by an effective
zero-dimensional field theory and can essentially be computed analytically. A
nontrivial flow of the spacetime curvature is induced either by a nonminimal
coupling to gravity or by self-interactions. The latter leads to a decrease of
the spacetime curvature through loop effects, which, for minimally coupled,
massless fields, grow unbounded in the infrared. However, such large loop
contributions are eventually screened by the dynamical generation of a
nonperturbative, gravitationally induced mass and the renormalisation of the
spacetime curvature saturates to a nonzero value. Finally, we show that, in the
case of spontaneously broken continuous symmetries, the Goldstone modes do not
contribute to the infrared flow of the spacetime curvature, despite being
strongly amplified by the gravitational field.
