Dark energy perturbations in N-body simulations

Abstract

We present N -body simulations which are fully compatible with general relativity, with dark energy consistently included at both the background and perturbation level. We test our approach for dark energy parameterised as both a fluid, and using the parameterised post-Friedmann (PPF) formalism. In most cases, dark energy is very smooth relative to dark matter so that its leading effect on structure formation is the change to the background expansion rate. This can be easily incorporated into Newtonian N -body simulations by changing the Friedmann equation. However, dark energy perturbations and relativistic corrections can lead to differences relative to Newtonian N -body simulations at the tens of percent level for scales k < (10 −3 -10 −2 ) Mpc −1 , and given the accuracy of upcoming large scale structure surveys such effects must be included. In this paper we will study both effects in detail and highlight the conditions under which they are important. We also show that our N -body simulations exactly reproduce the results of the Boltzmann solver class for all scales which remain linear. arXiv:1904.05210v1 [astro-ph.CO]

Euclid preparation: IX. EuclidEmulator2 – power spectrum emulation with massive neutrinos and self-consistent dark energy perturbations

“…Here we shall just briefly recap the key aspects of the theory of time-dependent DE relevant in the context of EuclidEmula-tor2. We shall follow closely the explanations given in Dakin et al (2019b) where this topic has been reviewed in greater detail. There are two popular ways of describing DE in the setting of an effective theory: the fluid description and the so-called parametrized post-Friedmann (PPF) description (Hu & Sawicki 2007).…”

“…Although this value is close to the best fitting value from supernova surveys (Betoule et al 2014), DE with a slightly time-dependent equation of state parameter is not ruled out by the data currently available. The effects of DE perturbations become relevant only on the largest scales (usually at 0.1 ℎ Mpc −1 ) as has recently been studied carefully in Dakin et al (2019b). Nevertheless, the effects of DE on the matter power spectrum can become quite significant, primarily because changes in the DE component have an impact on the scale factor ( ) which in turn affects the power spectrum on all scales.…”

“…As can be seen in Equation (2.9) in Dakin et al (2019b), the Euler equation for a DE fluid features a factor (1 + ) −1 , leading to divergences for cosmologies with a DE equation of state (EoS) parameter that evolves across 1 + = 0 over time. This is a manifestation of the fact that such a DE is gravitationally unstable for the lack of additional internal degrees of freedom (Fang et al 2008).…”

“…In the last equation, in turn, N t denotes the velocity divergence field of all other species than DE in the conformal Newtonian gauge. For a more complete discussion we refer the reader to Dakin et al (2019b), section 2.1.2.…”

Clustering dark energy imprints on cosmological observables of the gravitational field

“…As discussed in Hassani et al (2019), although we keep only linear terms in the scalar field dynamics and we drop higher order selfinteractions of π , the scalar field does cluster and form non-linear scalar field structures in k-evolution because it is sourced by nonlinearities in matter through gravitational coupling. This is the crucial improvement over the treatment of dark energy in GEVOLUTION, which uses the transfer functions from linear theory to keep track of perturbations in the dark energy fluid similar to how it is done in Dakin et al (2019) (see also Brando, Koyama & Wands 2020,fora more comprehensive extension of this framework to EFT).…”