Counting voids to probe dark energy

We show that the number of observed voids in galaxy redshift surveys is a sensitive function of the equation of state of dark energy. Using the Fisher matrix formalism we find the error ellipses in the $w_0-w_a$ plane when the equation of state of dark energy is assumed to be of the form $w_{CPL}(z)=w_0 +w_a z/(1+z)$. We forecast the number of voids to be observed with the ESA Euclid satellite and the NASA WFIRST mission, taking into account updated details of the surveys to reach accurate estimates of their power. The theoretical model for the forecast of the number of voids is based on matches between abundances in simulations and the analytical prediction. To take into account the uncertainties within the model, we marginalize over its free parameters when calculating the Fisher matrices. The addition of the void abundance constraints to the data from Planck, HST and supernova survey data noticeably tighten the $w_0-w_a$ parameter space. We thus quantify the improvement in the constraints due to the use of voids and demonstrate that the void abundance is a sensitive new probe for the dark energy equation of state.