  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 which 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.
