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. The new analysis still awaits peer review, but it already lays out the central claim clearly.

It matters because cosmology operates at the edge of what current instruments can measure, where systematic errors and model assumptions are never trivial. Small discrepancies between independent measurements have historically pointed toward missing physics rather than simple calibration errors, and the ongoing tension in the Hubble constant is a live example of how a persistent disagreement between methods can reshape the theoretical landscape. Each new dataset that approaches this territory with independent systematics adds real information to a problem that has resisted easy resolution for more than a decade. 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.

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. 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. 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. Minkowski functionals and moments provide comparable constraining power, while combining them with the other summaries gives the strongest constraints.

The relevance goes beyond one dataset because even small shifts in measured parameters can matter when the field is testing the limits of the standard cosmological model. The Lambda-CDM framework describes the observable universe with remarkable economy, but its success rests on two components, dark matter and dark energy, whose physical nature remains entirely unknown. Any credible measurement that tightens or loosens the constraints on those components moves the entire theoretical enterprise forward, regardless of whether the immediate result looks dramatic on its own terms.

Broad galaxy-lensing redshift coverage is particularly important for dynamical dark energy, while CMB lensing provides complementary information. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy.

Because this is still a preprint, the result should be read with genuine interest and proportionate caution. Peer review is not a guarantee of correctness, but it is a process that forces authors to respond to technical criticism from specialists who have no stake in a particular outcome. Preprints that survive that process, often with substantive revisions, emerge with a stronger evidential base than the version that first appeared. Until that stage is complete, the responsible reading keeps uncertainty explicitly visible rather than treating the claims as established findings.

The next step is to see whether the effect survives when independent surveys, different calibration strategies and tighter control of systematic uncertainties enter the picture. Programmes such as Euclid, DESI and the Rubin Observatory will deliver datasets over the next several years that cover the same parameter space with largely independent methods. If the current signal persists through those tests, its theoretical implications will become impossible to set aside. Until peer review and independent follow-up address those open questions, skepticism is not a failure of appreciation for the work; it is part of how science decides what to keep.

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