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The recently published analytic probability density function for the mildlynon-linear cosmic density field within spherical cells is used to build asimple but accurate maximum likelihood estimate for the redshift evolution ofthe variance of the density, which, as expected, is shown to have smallerrelative error than the sample variance. This estimator provides a competitiveprobe for the equation of state of dark energy, reaching a few percent accuracyon wp and wa for a Euclid-like survey. The corresponding likelihood functioncan take into account the configuration of the cells via their relativeseparations. A code to compute one-cell density probability density functionsfor arbitrary initial power spectrum, top-hat smoothing and various sphericalcollapse dynamics is made available online so as to provide straightforwardmeans of testing the effect of alternative dark energy models and initialpower-spectra on the low-redshift matter distribution.

Encircling the dark: constraining dark energy via cosmic density in spheres