Dynamical dark energy with AdS-to-dS and dS-to-dS transitions: Implications for the $H_0$ tension

Understand

We investigate the dynamics and cosmological implications of dark energy (DE), modeled as a scalar field with a hyperbolic tangent potential that induces a smooth shift in the effective cosmological constant (CC), encompassing transitions such as AdS-dS, 0-dS, and dS-dS, with the mirror AdS-dS as a particular case aligned with the $\Lambda_{\rm s}$CDM scenario.

• In our construction, a phantom scalar field with a negative kinetic term drives a bottom-up transition from an AdS-like vacuum at high redshifts to a dS-like vacuum at low redshifts, thereby providing a physical underpinning for the $\Lambda_{\rm s}$CDM scenario.
• Despite the negative kinetic term, the step-like form of the potential prevents pathologies such as unbounded energy growth, Big Rip, and violations of the WEC.
• Our numerical integration of the equations of motion shows that the model is consistent with both CMB data and the SH0ES determination of $H_0$, thereby addressing the $H_0$ tension, with all key kinematical parameters-$H(z)$, $\dot{H}(z)$, and $q(z)$-evolving smoothly.