Euclid: Modelling massive neutrinos in cosmology -- a code comparison

J. Adamek, R. E. Angulo, C. Arnold, M. Baldi, M. Biagetti, B. Bose, C. Carbone, T. Castro, J. Dakin, K. Dolag, W. Elbers, C. Fidler, C. Giocoli, S. Hannestad, F. Hassani, C. Hernández-Aguayo, K. Koyama, B. Li, R. Mauland, P. Monaco, C. Moretti, D. F. Mota, C. Partmann, G. Parimbelli, D. Potter, A. Schneider, S. Schulz, R. E. Smith, V. Springel, J. Stadel, T. Tram, M. Viel, F. Villaescusa-Navarro, H. A. Winther, B. S. Wright, M. Zennaro, N. Aghanim, L. Amendola, N. Auricchio, D. Bonino, E. Branchini, M. Brescia, S. Camera, V. Capobianco, V. F. Cardone, J. Carretero, F. J. Castander, M. Castellano, S. Cavuoti et al.

Submitted on 22 November 2022


The measurement of the absolute neutrino mass scale from cosmological large-scale clustering data is one of the key science goals of the Euclid mission. Such a measurement relies on precise modelling of the impact of neutrinos on structure formation, which can be studied with N-body simulations. Here we present the results from a major code comparison effort to establish the maturity and reliability of numerical methods for treating massive neutrinos. The comparison includes eleven full N-body implementations (not all of them independent), two N-body schemes with approximate time integration, and four additional codes that directly predict or emulate the matter power spectrum. Using a common set of initial data we quantify the relative agreement on the nonlinear power spectrum of cold dark matter and baryons and, for the N-body codes, also the relative agreement on the bispectrum, halo mass function, and halo bias. We find that the different numerical implementations produce fully consistent results. We can therefore be confident that we can model the impact of massive neutrinos at the sub-percent level in the most common summary statistics. We also provide a code validation pipeline for future reference.


Comment: 43 pages, 17 figures, 2 tables; published on behalf of the Euclid Consortium; data available at

Subject: Astrophysics - Cosmology and Nongalactic Astrophysics


Overview of the numerical codes employed in this code comparison. $N$-body codes typically use a particle-mesh (PM) method coupled to some scheme to increase the force resolution in high-density regions. Methods featured here include Tree-PM, adaptive mesh refinement (AMR), fast multipole method (FMM), particle-particle/particle-mesh (P$^3$M), and moving mesh. No adaptive force computation is used in \gevolution, \COLA, and \PINOCCHIO, which all work with a uniform mesh. : Overview of the basic parameters used in our simulation suite. The cases with $\sum m_\nu = 0\,\mathrm{eV}$ and $\sum m_\nu = 0.15\,\mathrm{eV}$ are the two main baselines for our comparison, but we include some cases with larger masses, up to $\sum m_\nu = 0.6\,\mathrm{eV}$, to probe more ``extreme'' regions of parameter space.