Probing dark energy with tomographic weak-lensing aperture mass
  statistics
  We forecast and optimize the cosmological power of various weak-lensing
aperture mass ($M_{\rm ap}$) map statistics for future cosmic shear surveys,
including peaks, voids, and the full distribution of pixels (1D $M_{\rm ap}$).
These alternative methods probe the non-Gaussian regime of the matter
distribution, adding complementary cosmological information to the classical
two-point estimators. Based on the SLICS and cosmo-SLICS $N$-body simulations,
we build Euclid-like mocks to explore the $S_8 - \Omega_{\rm m} - w_0$
parameter space. We develop a new tomographic formalism which exploits the
cross-information between redshift slices (cross-$M_{\rm ap}$) in addition to
the information from individual slices (auto-$M_{\rm ap}$) probed in the
standard approach. Our auto-$M_{\rm ap}$ forecast precision is in good
agreement with the recent literature on weak-lensing peak statistics, and is
improved by $\sim 50$% when including cross-$M_{\rm ap}$. It is further boosted
by the use of 1D $M_{\rm ap}$ that outperforms all other estimators, including
the shear two-point correlation function ($\gamma$-2PCF). When considering all
tomographic terms, our uncertainty range on the structure growth parameter
$S_8$ is enhanced by $\sim 45$% (almost twice better) when combining 1D $M_{\rm
ap}$ and the $\gamma$-2PCF compared to the $\gamma$-2PCF alone. We additionally
measure the first combined forecasts on the dark energy equation of state
$w_0$, finding a factor of three reduction of the statistical error compared to
the $\gamma$-2PCF alone. This demonstrates that the complementary cosmological
information explored by non-Gaussian $M_{\rm ap}$ map statistics not only
offers the potential to improve the constraints on the recent $\sigma_8$ -
$\Omega_{\rm m}$ tension, but also constitutes an avenue to understand the
accelerated expansion of our Universe.
