A new study has analyzed the shape of three-dimensional and projected dark-matter halo profiles, extracted from cosmological $N$-body simulations. The work focuses on the standard $\Lambda$CDM cosmological model and non-standard cosmologies, including massive neutrinos, $f(\mathcal{R})$ gravity, and dynamical dark energy. This analysis is crucial for the Euclid mission, as it quantifies the differential imprint of non-standard physics on halo structure, a fundamental aspect for the cluster weak-lensing studies that the space telescope will perform.

The researchers used the DUSTGRAIN-PF and DEMNUni simulation suites, comparing density, mass, velocity-dispersion, and excess-surface-density profiles up to $5\,r_{500{ m c}}$. The main analysis was performed at a redshift $z=1.1$, a high-$z$ regime where the weak-lensing signal-to-noise begins to degrade, providing a conservative stress test for detectability. In low-mass halos ($M_{ m 200c}<7 imes10^{13}\,M_\odot$), $f(\mathcal{R})$ gravity produces deviations of about $10\,\%$ in projected and three-dimensional profiles, especially in the outskirts where screening is less efficient. Massive neutrinos partially reduce this signal, reflecting the competition between free streaming and fifth-force-enhanced growth.

Cosmologies with dynamical dark energy and massive neutrinos generally induce smaller, few-percent deviations, with the largest effects again found in low-mass halos and at large radii. Under simplified assumptions for Euclid weak lensing, detecting such profile differences at $z=1.1$ requires stacks of approximately $10^5$ halos, while a few thousand halos may be sufficient at $z\lesssim0.5$. This underscores the need to integrate precise modeling of these non-standard effects into any likelihood analysis involving Euclid weak-lensing masses, to avoid non-negligible systematic biases. Concentration-mass relations show weaker cosmological dependence, typically at about the $5\,\%$ level.