General relativistic screening in cosmological simulations
- Author(s)
- Oliver Hahn, Aseem Paranjape
- Abstract
We revisit the issue of interpreting the results of large volume cosmological simulations in the context of large-scale general relativistic effects. We look for simple modifications to the nonlinear evolution of the gravitational potential ψ that lead on large scales to the correct, fully relativistic description of density perturbations in the Newtonian gauge. We note that the relativistic constraint equation for ψ can be cast as a diffusion equation, with a diffusion length scale determined by the expansion of the Universe. Exploiting the weak time evolution of ψ in all regimes of interest, this equation can be further accurately approximated as a Helmholtz equation, with an effective relativistic "screening" scale ℓ related to the Hubble radius. We demonstrate that it is thus possible to carry out N-body simulations in the Newtonian gauge by replacing Poisson's equation with this Helmholtz equation, involving a trivial change in the Green's function kernel. Our results also motivate a simple, approximate (but very accurate) gauge transformation—δN(k )≈δsim(k )×(k2+ℓ-2)/k2 —to convert the density field δsim of standard collisionless N -body simulations (initialized in the comoving synchronous gauge) into the Newtonian gauge density δN at arbitrary times. A similar conversion can also be written in terms of particle positions. Our results can be interpreted in terms of a Jeans stability criterion induced by the expansion of the Universe. The appearance of the screening scale ℓ in the evolution of ψ , in particular, leads to a natural resolution of the "Jeans swindle" in the presence of superhorizon modes.
- Organisation(s)
- Department of Astrophysics, Department of Mathematics
- External organisation(s)
- Université Côte d'Azur, Inter-University Centre for Astronomy and Astrophysics India
- Journal
- Physical Review D
- Volume
- 94
- Pages
- 83511
- ISSN
- 2470-0010
- DOI
- https://doi.org/10.1103/PhysRevD.94.083511
- Publication date
- 10-2016
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 103044 Cosmology, 103028 Theory of relativity
- Portal url
- https://ucrisportal.univie.ac.at/en/publications/0a0629ba-0d4e-4531-b363-0b9c2c58f09b