The Sign-Switching of the Cosmological Constant

Abstract

We propose and investigate a class of dynamical dark energy models in which the cosmological constant evolves from negative values in the early Universe to a positive value at low redshifts. This framework includes a generalised ladder-step evolution, as well as smooth-transition scenarios, providing a unified description of sign-changing cosmological constants. We analyse the theoretical construction and background dynamics of these models using cosmographic diagnostics. Extending this study to the linear perturbation regime, we solve the perturbation equations from the radiation-dominated era with adiabatic initial conditions. We examine the evolution of the matter density contrast, gravitational potential, and the $fσ_8$ observable. Our results are compared against the standard $Λ$CDM model and confronted with current observational data, illustrating the phenomenological viability of sign-changing dark energy models and revealing distinctive imprints on cosmic structure formation arising from the transition of the cosmological constant.

Figures (5)

• Figure 1: The left figure showcases the total EoS parameter, $w_{\mathrm{tot}}(z)$, against redshift. The right figure showcases the evolution of DE energy density. The bottom figures showcases $H(z)$ in units of $km/s/Mpc$ against redshift. The the error bars were obtained from Ref. Favale:2023lnp. The vertical black line denotes the sign-switching redshift for the DE density.
• Figure 2: Comparison of the cosmographic parameters $q(z)$, $j(z)$, $s(z)$ and $l(z)$ for the different models. The vertical line denotes the redshift at which the DE density changes sign.
• Figure 3: Evolution of fractional energy density perturbations in matter, $\delta_m$, for all sign-switching models (continuous lines) compared against $\Lambda$CDM (dashed lines). Each colour corresponds to a different Fourier mode:k = 3.33 $\times 10^{-4}$ h Mpc$^{-1}$ (Yellow), k = 1.04 $\times10^{-3}$ h Mpc$^{-1}$ (Green-yellow), k = 3.27$\times10^{-3}$ h Mpc$^{-1}$ (Green), k = $1.02 \times10^{-2}$ h Mpc$^{-1}$ (Cyan), k = 3.19$\times10^{-2}$ h Mpc$^{-1}$ (Blue), k = 0.1 h Mpc$^{-1}$ (Purple). The dashed left vertical line indicates the radiation-matter equality, the right one the matter–DE equality, and the dotted vertical line between them corresponds to the sign-switching redshift.
• Figure 4: Gravitational potential $\Psi/\Psi_{\rm i}$, for all sign-switching models (continuous lines) compared against $\Lambda$CDM (dashed lines). Each colour corresponds to a different Fourier mode: k = 3.33 $\times 10^{-4}$ h Mpc$^{-1}$ (Yellow), k = 1.04 $\times10^{-3}$ h Mpc$^{-1}$ (Green-yellow), k = 3.27$\times10^{-3}$ h Mpc$^{-1}$ (Green), k = $1.02 \times10^{-2}$ h Mpc$^{-1}$ (Cyan), k = 3.19$\times10^{-2}$ h Mpc$^{-1}$ (Blue), k = 0.1 h Mpc$^{-1}$ (Purple). The dashed right vertical line indicates the matter–DE equality, and the dotted left vertical line corresponds to the sign-switching redshift.
• Figure 5: The left columns corresponds to the evolution of $f \sigma_8$ for redshift between $z=0$ and $z=2$ against the data points of Ref. Avila:2022xad. The continuous lines correspond to the respective models of study while the dashed ones to $\Lambda$CDM. The right column corresponds to the ratio of $f\sigma8$ of each models against $\Lambda$CDM.