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Abstract. The standard model of cosmology, known as LCDM, has a great success in interpretation of the cosmological observations from cosmic microwave background (CMB) radiation to the large scale structure (LSS) observation. However, there are a couple of tensions between the observations and theory. One category of these challenges is in the galactic scale known as "core-cusp", "missing satellite" and "too big too fail" problems. On the other hand, the measurement of the Hubble parameter from CMB and nearby supernovae are in tension. In this talk, I will present the idea of how the non-linear structure formation and the characteristics of the cosmic web can be used to study these tensions and their probable solutions in more detail. Accordingly, I will introduce the non-Markov version of the excursion set theory as an analytical approach to study the non-linear structures, and then I will show how the idea of the modified initial condition can address the galactic scale challenges of the LCDM. In the next part of the talk I will show, how the Hubble parameter tension can be related to the structure formation history and the merger rate of dark matter halos, which can be considered as a complementary observation to study the tension and its observational consequences in LSS.
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