Dictionary-free handling of all-scale cosmological perturbations

Gravitational clustering of cold dark matter, as predicted by concordance cosmology, is often studied via N-body simulations based on Newtonian dynamics. Though efficient in tracking nonlinear growth of fluctuations at small scales, outcomes of such simulations cannot be linked to observables immediately, and a certain effort is required to obtain relativistic interpretations of variables by employing convenient gauges and dictionaries. Based on a weak-field expansion of general relativity, a fully-relativistic N-body code has been introduced in the past decade (Adamek, J., Daverio, D., Durrer, R., Kunz, M., JCAP 07, 053 (2016)), capable of evolving all metric variables in the Poisson gauge which is the conventional choice in formulating cosmological perturbations. However, spatial and temporal derivates are assigned different orders of smallness and field equations, containing admixtures of higher-order terms, acquire a rather complex form. In this talk we will explore an alternative formulation of perturbations, still based on a weak-field expansion, and expressed in the Poisson gauge, which however treats all derivates on equal footing and hence a clear distinction exists between first and second order contributions in the expansion (Eingorn, M., ApJ 825, 84 (2016), Canay, E., Eingorn, M., PDU 29, 100565 (2020), arXiv:2206.13495 [gr-qc]). We will show that it is possible to obtain analytical solutions for the scalar and vector potentials in this scheme and that they hint at some exciting characteristics of gravitational interactions at large-enough cosmological scales.