Mass assembly history of dark matter halos in the light of $H_0$ tension

Monthly Notices of the Royal Astronomical Society, Volume 511, Issue 2, April 2022, Pages 1601,1608 The Hubble tension may introduce a new course of action to revise the standard $\Lambda$CDM model to unravel dark energy and dark matter physics. The Hubble parameter can be reconstructed by late-time observations of the background evolution model independently. We relate the reconstructed Hubble parameter to the structure formation and large scale structure observables in this work. We use the excursion set theory to calculate the number density of dark matter halos and the mass function of progenitors. We obtain the results for both the Markov and non-Markov extension of the excursion set theory in the context of spherical and ellipsoidal collapse. We show that the number density of dark matter halos in the reconstructed model has approximately $\sim2\sigma$ difference in comparison to the Planck-2018 $\Lambda$CDM in the mass range of $M\gtrsim10^{12}M_{\odot}$. We also compare the dark matter halo progenitor mass function with the pair-galaxy statistics and their mass assembly history from observational data of the HST, CANDEL survey. Due to complications to distinguish the ratio of accretion and merger in mass assembly, our result on pair fraction is for illustration only. However, a $\sim5$ times more accurate observations will be promising to distinguish the reconstructed model and the Planck-2018 $\Lambda$CDM.