The Sign-Switching of the Cosmological Constant

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 $f\sigma_8$ observable. Our results are compared against the standard $\Lambda$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.