We explore the predictions of ${\mathrm{\Lambda }}_{\mathrm{s}}\mathrm{CDM}$, a novel framework suggesting a rapid anti–de Sitter (AdS) to de Sitter (dS) vacua transition in the late Universe, on bound cosmic structures. In its simplest version, the cosmological constant ${\mathrm{\Lambda }}_{\mathrm{s}}$ abruptly switches sign from negative to positive, attaining its present-day value at a redshift of $z_{†}\sim 2$. The ${\mathrm{\Lambda }}_{\mathrm{s}}\mathrm{CDM}$ model emerges as a promising solution to major cosmological tensions, particularly the $H_0$ and $S_8$ tensions, as well as other less definite tensions. A key aspect of our investigation is examining the impact of the abrupt ${\mathrm{\Lambda }}_{\mathrm{s}}\mathrm{CDM}$ model on the formation and evolution of bound cosmic structures. We identify three primary influences: (i) the negative cosmological constant (AdS) phase for $z>z_{†}$, (ii) the abrupt transition marked by a type-II (sudden) singularity, leading to an abrupt increase in the Universe’s expansion rate at $z=z_{†}$, and (iii) an increased expansion rate in the late Universe under a positive cosmological constant for $z<z_{†}$, compared to $\mathrm{\Lambda }\mathrm{CDM}$. Utilizing the spherical collapse model, we investigate the nonlinear evolution of bound cosmic structures within the ${\mathrm{\Lambda }}_{\mathrm{s}}\mathrm{CDM}$ framework. We find that the virialization process of cosmic structures and, consequently, their matter overdensity vary depending on whether the AdS-dS transition precedes or follows the turnaround. Specifically, structures virialize with either increased or reduced matter overdensity compared to the Planck-$\mathrm{\Lambda }\mathrm{CDM}$ model, contingent on the timing of the transition. Additionally, our results demonstrate that the sudden singularity does not result in the dissociation of bound systems. Despite its profound nature, the singularity exerts only relatively weak effects on such systems, thereby reinforcing the model’s viability in this context.

• Received 16 February 2024
• Accepted 8 April 2024

DOI:https://doi.org/10.1103/PhysRevD.109.103522