ΛCDM Tensions: Localising Missing Physics through Consistency Checks

(Formula presented.) CDM tensions are by definition model-dependent; one sees anomalies through the prism of (Formula presented.) CDM. Thus, progress towards tension resolution necessitates checking the consistency of the (Formula presented.) 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 (Formula presented.) 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 (Formula presented.) CDM model fitting parameters. We highlight the recent progress made on (Formula presented.) tension and elucidate how similar progress can be made on (Formula presented.) tension. Our discussions indicate that (Formula presented.) tension, equivalently a redshift-dependent (Formula presented.), and a redshift-dependent (Formula presented.) imply a problem with the background (Formula presented.) CDM cosmology.