Backreaction of super-Hubble cosmological perturbations beyond perturbation theory

We discuss the effect of super-Hubble cosmological fluctuations on the locally measured Hubble expansion rate. We consider a large bare cosmological constant in the early Universe in the presence of scalar field matter (the dominant matter component), which would lead to a scale-invariant primordial spectrum of cosmological fluctuations. Using the leading-order gradient expansion, we show that the expansion rate measured by a (secondary) clock field which is not comoving with the dominant matter component obtains a negative contribution from infrared fluctuations, a contribution whose absolute value increases in time. This is the same effect that a decreasing cosmological constant would produce. This supports the conclusion that infrared fluctuations lead to a dynamical relaxation of the cosmological constant. Our analysis does not make use of any perturbative expansion in the amplitude of the inhomogeneities.