Cosmological perturbations for smooth sign-switching dark energy models

TL;DR

This work analyzes linear cosmological perturbations in four sign-switching dark energy models that modify the late-time cosmological constant while keeping the background evolution close to ΛCDM. The authors formulate the perturbation equations in the Newtonian gauge for a multi-fluid Universe and apply adiabatic initial conditions set in the radiation era, solving for modes well outside the horizon. They examine the evolution of the matter density contrast $\delta_m$, the gravitational potential $\Psi$, the growth observable $f\sigma_8$, and the matter power spectrum, comparing to ΛCDM and Planck-era data. The main result is that, at linear order, all four models closely track ΛCDM, with only mild imprints during the sign-switch transitions, suggesting viability under current structure-formation constraints.

Abstract

In this work, we carry out a comprehensive perturbative analysis of four cosmological models featuring a sign-switching cosmological constant. Among these, we include the well-known $Λ_{\rm s}$CDM model, characterised by an abrupt transition from a negative to a positive cosmological constant. We also consider the L$Λ$CDM model, which exhibits a generalised ladder-step evolution, as well as the SSCDM and ECDM models, both of which undergo a smooth sign change at comparable redshifts. We solve the linear cosmological perturbation equations from the radiation-dominated era, imposing initial adiabatic conditions for matter and radiation, for modes well outside the Hubble radius in the early Universe. We analyse the behaviour of the matter density contrast, the gravitational potential, the linear growth rate, the matter power spectrum, and the $fσ_8$ evolution . These results are contrasted with predictions from the standard $Λ$CDM model and are confronted with observational data.

Figures (2)

• Figure 1: Evolution of matter perturbations, $\delta_m$, for the four sign-switching models, compared with the standard $\Lambda$CDM scenario. In all four cases, the behaviour of the perturbations closely resembles that of $\Lambda$CDM, rendering the models largely indistinguishable in this respect. In each panel, solid lines correspond to the model under consideration, while dotted lines represent the $\Lambda$CDM predictions. Different colours denote distinct Fourier modes: $k = 3.33 \times 10^{-4} \ \text{h} \ \text{Mpc}^{-1}$ (Dark Gray-Green), $k = 1.04 \times 10^{-3} \ \text{h} \ \text{Mpc}^{-1}$ (Deep Green), $k = 3.27 \times 10^{-3} \ \text{h} \ \text{Mpc}^{-1}$ (Dark Teal), $k = 1.02 \times 10^{-2} \ \text{h} \ \text{Mpc}^{-1}$ (Turquoise), $k = 3.19 \times 10^{-2} \ \text{h} \ \text{Mpc}^{-1}$ (Teal Green), $k = 0.1 \ \text{h} \ \text{Mpc}^{-1}$ (Aqua Blue). The perturbations are plotted as a function of $x = \ln(a/a_0)$, ranging from the radiation-dominated era ($x = -15$) to the far future ($x = 12$), with $x = 0$ corresponding to the present time. The left dashed vertical line marks the radiation–matter equality, the right dashed line indicates the matter–DE equality, and the solid vertical line denotes the redshift at which the DE density changes sign.
• Figure 2: