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Structures in the Universe are arranged into the cosmic web. Distributions,statistics, and evolutions of the structures can be used as probes forcosmological models. We investigate the number density of voids and dark matterhalos-in-voids in the Excursion Set Theory (EST). We study the Markov andnon-Markov frameworks of EST in both spherical and ellipsoidal collapse models.Afterward, we compare the number density of voids and halos-in-voids in thestandard $\Lambda$CDM and the reconstructed model. The reconstructed model is amodel-independent reconstruction based on background observations. This workexplores the effects of the collapse model barrier in the different ESTframeworks on the statistics of voids and the statistics of halos-in-voids.Finally, we find the hint that cosmological models can be distinguished by thenumber density of halos-in-voids in the $1.0-2.5$ redshift range. The maximumdifference is observed in $z\sim1.9$.

Voids and Halos in Voids statistics as a probe of the Expansion History of the Universe