Assessing the growth of structure over cosmic time with cosmic microwave background lensing

The standard [Formula: see text]-Cold Dark Matter cosmological model informed by cosmic microwave background (CMB) anisotropies makes a precise prediction for the growth of matter density fluctuations over cosmic time on linear scales. A variety of cosmological observables offer independent and complementary ways of testing this prediction, but results have been mixed, with many constraints on the amplitude of structure [Formula: see text] being 2-3[Formula: see text] lower than the expectation from Planck primary CMB anisotropies. It is currently unclear whether these discrepancies are due to observational systematics, nonlinearities and baryonic effects or new physics. We review how gravitational lensing of the CMB has and will continue to provide insights into this problem, including through tomographic cross-correlations with galaxy surveys over cosmic time.This article is part of the discussion meeting issue 'Challenging the standard cosmological model'.