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We present the merging of the Particle-Mesh (PM) relativistic gevolution code with the TreePM gadget-4 code, with the aim of studying general relativity effects in cosmology. Our code, called grgadget , is able to track the evolution of metric perturbations in the weak field limit by using gevolution 's implementation of a relativistic PM in the Poisson gauge. To achieve this, starting from gevolution , we have written a c++ library called libgevolution , which allows a code to access and use the same abstractions and resources that gevolution uses for its PM-only N -body simulations. The code works under the assumption that particle interactions at short distances can be approximated as Newtonian, so that we can combine the forces computed with a Newtonian Tree with those computed with a relativistic PM. The result is a TreePM simulation code that represents metric perturbations at the scales where they are relevant while resolving non-linear structures. We validate our code by closely matching gadget-4 forces, computed with the Tree switched off, with those computed with libgevolution in the Newtonian limit. With grgadget , we obtain a matter power spectrum that is compatible with Newtonian gadget-4 at small scales and contains GR features at large scales that are consistent with results obtained with gevolution. We demonstrate that, due to the better resolution of the highly non-linear regime, the representation of the relativistic fields sampled on the mesh improves with respect to the PM-only simulations. [ABSTRACT FROM AUTHOR]

We present a perturbative treatment of non-linear galaxy clustering in the context of the cubic Galileon modified gravity model, in terms of second-order Lagrangian Perturbation theory and an extension of ellipsoidal collapse that includes Vainshtein screening. We numerically implement such prescriptions in the approximate pinocchio code, and use it to generate realizations of the matter density field and halo catalogues with different prescriptions for ellipsoidal collapse. We investigate the impact of three different approximations in the computation of collapse times on the halo mass function, halo bias, and matter power spectrum. In the halo mass function, both the modified gravity effect and the screening effect are significant in the high-mass end, similar to what is found for other MG models. We perform a comparison with N -body simulations to assess the validity of our approach, and show that we can reproduce the same trend observed in simulations for all quantities considered. With a simple modification to the grouping algorithm of pinocchio to take into account the gravity modification, and without the need to re-calibrate the algorithm, we show that we can reproduce the linear halo bias and the mildly non-linear matter power spectrum of simulations with good accuracy, especially for the implementation with Vainshtein screening. We stress that, while approximate, our method is orders of magnitude faster than a full N -body simulation, making it an optimal tool for the quick generation of large sets of halo catalogues for cosmological observables. [ABSTRACT FROM AUTHOR]