Non-linear Structure Formation for Dark Energy Models with a Steep Equation of State

TL;DR

This paper investigates the nonlinear structure formation in dynamical dark energy models with a steep equation of state, modifying a simulation code to analyze deviations from the standard cosmological model in matter power spectrum, halo mass function, and correlation functions.

Contribution

It introduces a modified L-PICOLA code to efficiently explore nonlinear effects of a steep dark energy equation of state on large-scale structure formation.

Findings

Steep transition models show minimal deviation (~2-4%) from ΛCDM in power spectrum.

Halo mass function can distinguish high-mass end differences between models.

Significant deviations observed in nonlinear growth for models with only background and linear perturbations.

Abstract

We study the nonlinear regime of large scale structure formation considering a dynamical dark energy (DE) component determined by a Steep Equation of State parametrization (SEoS) $w(z)=w_0+w_i\frac{(z/z_T)^q}{1+(z/z_T)^q}$. In order to perform the model exploration at low computational cost, we modified the public code L-PICOLA. We incorporate the DE model by means of the first and second-order matter perturbations in the Lagrangian frame and the expansion parameter. We analyze deviations of SEoS models with respect to $\Lambda$CDM in the non-linear matter power spectrum ($P_k$), the halo mass function (HMF), and the two-point correlation function (2PCF). On quantifying the nature of steep (SEoS-I) and smooth transitions in DE field (CPL-lim), no signature of steep transition is observed, rather found the overall impact of DE behaviors in $P_k$ at level of $\sim 2-3\%$ and $\sim 3-4\%$ differences w.r.t $\Lambda$CDM at $z=0$ respectively. HMF shows the possibility to distinguish between the models at the high mass ends. The best-fitted model assuming only background and linear perturbations dubbed as SEoS-II largely deviates from $\Lambda$CDM and current observations on studying the nonlinear growth. This large deviation in SEoS-II also quantified the combined effect of the dynamical DE and the larger amount of matter contained, $\Omega_{m0}$ and $H_{0}$ accordingly. 2PCF results are relatively robust with $\sim 1-2 \%$ deviation for SEoS-I and CPL-lim and a significant deviation for SEoS-II throughout $r$ from $\Lambda$CDM. Finally, we conclude that the search for viable DE models (like the SEoS) must include non-linear growth constraints.