Abundance of cosmic voids in EFT of dark energy

Abstract Cosmic voids in the large-scale structure are among the useful probes for testing gravity on cosmological scales. In this paper, we investigate the evolution of voids in the Horndeski theory using the effective field theory (EFT) of dark energy. Modeling the void formation with the dynamics of spherical mass shells, we study how modifications of gravity encoded into the EFT of dark energy change the linearly extrapolated critical density contrast that is relevant for the criterion for void formation, with particular focus on the time-dependent parameter characterizing the effect of kinetic braiding. It is found that the change in the critical density contrast is one order of magnitude smaller than the dimensionless EFT parameter because of a slight imbalance between two compensating effects. We then compute the void abundance using the Sheth-van de Weygaert void size function and demonstrate that it exhibits scale-dependent modifications. It is shown that the modifications to the void size function on small scales are almost entirely determined by the modified linear matter power spectrum, while the modifications on large scales are dominated by the contributions from the linear matter spectrum and the critical density contrast.