Late-time suppression of structure growth as a solution for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>8</mml:mn> </mml:msub> </mml:math> tension

The ${S}_{8}$ value inferred from the Subaru Hyper Suprime-Cam (HSC) Year 3 cosmic shear data, under the assumption of the flat $\mathrm{\ensuremath{\Lambda}}$ cold dark matter ($\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$) model, is $2--3\ensuremath{\sigma}$ lower than that inferred from observations of the early-time Universe, such as cosmic microwave background (CMB) anisotropy data. Resolving the ${S}_{8}$ tension requires a scenario in which structure formation on small scales is suppressed in the late Universe. As potential solutions, we consider extended models both within and beyond the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model---models that incorporate parametrized baryonic feedback effects, the effect of varying neutrino mass, and modified structure growth, each of which can lead to a suppression of structure growth at lower redshifts, with its own distinct scale and redshift dependencies. In particular, we consider phenomenological modified gravity models in which the suppression of structure growth is triggered at lower redshifts, as dark energy ($\mathrm{\ensuremath{\Lambda}}$) begins to dominate the background expansion. We show that the modified growth factor models---especially those featuring more rapid growth suppression at lower redshifts---provide an improved fit to the combined datasets of the HSC-Y3 cosmic shear correlation functions, the Planck CMB, and the ACT DR6 CMB lensing, compared to the fiducial $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model and the models including the baryonic effects or the massive neutrino effect within the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ framework.