Modelling Non-Linear Effects of Dark Energy

Abstract

We investigate the capabilities of perturbation theory in capturing non-linear effects of dark energy. We test constant and evolving $\omega$ models, as well as models involving momentum exchange between dark energy and dark matter. Specifically, we compare perturbative predictions at 1-loop level against N-body results for four non-standard equations of state as well as varying degrees of momentum exchange between dark energy and dark matter. The interaction is modelled phenomenologically using a time dependent drag term in the Euler equation. We make comparisons at the level of the matter power spectrum and the redshift space monopole and quadrupole. The multipoles are modelled using the Taruya, Nishimichi and Saito (TNS) redshift space spectrum. We find perturbation theory does very well in capturing non-linear effects coming from dark sector interaction. We isolate and quantify the 1-loop contribution coming from the interaction and from the non-standard equation of state. We find the interaction parameter $\xi$ amplifies scale dependent signatures in the range of scales considered. Non-standard equations of state also give scale dependent signatures within this same regime. In redshift space the match with N-body is improved at smaller scales by the addition of the TNS free parameter $\sigma_v$. To quantify the importance of modelling the interaction, we create mock data sets for varying values of $\xi$ using perturbation theory. This data is given errors typical of Stage IV surveys. We then perform a likelihood analysis using the first two multipoles on these sets and a $\xi=0$ modelling, ignoring the interaction. We find the fiducial growth parameter $f$ is generally recovered even for very large values of $\xi$ both at $z=0.5$ and $z=1$. The $\xi=0$ modelling is most biased in its estimation of $f$ for the phantom $\omega=-1.1$ case.