ΛCDM Tensions: Localising Missing Physics through Consistency Checks

Lambda CDM tensions are by definition model-dependent; one sees anomalies through the prism of Lambda CDM. Thus, progress towards tension resolution necessitates checking the consistency of the Lambda CDM model to localise missing physics either in redshift or scale. Since the universe is dynamical and redshift is a proxy for time, it is imperative to first perform consistency checks involving redshift, then consistency checks involving scale as the next steps to settle the "systematics versus new physics" debate and foster informed model building. We present a review of the hierarchy of assumptions underlying the Lambda CDM cosmological model and comment on whether relaxing them can address the tensions. We focus on the lowest lying fruit of identifying missing physics through the identification of redshift-dependent Lambda CDM model fitting parameters. We highlight the recent progress made on S8:=sigma 8 Omega m/0.3 tension and elucidate how similar progress can be made on H0 tension. Our discussions indicate that H0 tension, equivalently a redshift-dependent H0, and a redshift-dependent S8 imply a problem with the background Lambda CDM cosmology.