Constraining Dynamical Dark Energy with Tomographic Galaxy and CMB Weak Lensing Through Higher-Order Statistics

Tomographic weak gravitational lensing probes cosmic structure growth and geometry, making it a powerful probe of dynamical dark energy. We forecast information beyond the lensing power spectrum from non-Gaussian statistics of tomographic galaxy and CMB lensing convergence maps. Using the $\texttt{DDELenS}$ suite of ray-traced $N$-body simulations, we build Gaussian process emulators for power spectra, Minkowski functionals, moments, peak and minima counts, and the wavelet scattering transform, varying $Ω_m$, $σ_8$, $w_0$, and $w_a$. We consider Rubin-like galaxy lensing and Simons Observatory-like CMB lensing over $15{,}000\,\mathrm{deg}^2$, and validate the analysis using a withheld fiducial cosmology, analytical power-spectrum forecasts, and Gaussian random-field null tests. As an initial step, we neglect baryonic effects and intrinsic alignments and approximate galaxy sources as discrete redshift planes. Using all source redshifts at $z_s=\{0.5, 1, 1.5, 2, 2.5, 1100\}$, combining all five non-Gaussian statistics reduces uncertainties on $w_0$ and $w_a$ by $24.3\%$ and $28.0\%$, and on $Ω_m$ and $σ_8$ by $41.9\%$ and $45.8\%$, relative to the power-spectrum-only baseline. The resulting $w_0$ and $w_a$ uncertainties are $34.7\%$ and $48.7\%$ smaller than current DESI+DES constraints. If the DESI+DES best-fit values remain unchanged, this precision would increase the significance of the departure from $Λ$CDM from $3.0σ$ to $5.2σ$, compared with $3.8σ$ from the power spectrum alone, assuming a Gaussian posterior and unchanged $w_0$–$w_a$ correlation. Minkowski functionals and moments provide comparable constraining power, while combining them with the other summaries gives the strongest constraints. Broad galaxy-lensing redshift coverage is particularly important for dynamical dark energy, while CMB lensing provides complementary information.