How does Inflation Affect Renting vs. Buying a Home?

[Charles Lecky]

How does the inflation rate affect the renting versus buying home? What does it directly affect (i.e., the security deposit, the monthly mortgage payment, the monthly rent payment, the annual appreciation of a home)? I am having some confusion after using Nerdwallet and Smartasset's Rent vs. Buy calculator since I am trying to use a spreadsheet myself and understand WHAT and HOW inflation directly affects these two decisions.  Please be concrete on the explanation. Thank you