Mapping the $\Lambda_{\rm s}$CDM scenario to $f(T)$ modified gravity: Effects on structure growth rate

Understand

The concept of a rapidly sign-switching cosmological constant, interpreted as a mirror AdS-dS transition in the late universe and known as the $\Lambda_{\rm s}$CDM, has significantly improved the fit to observational data, offering a promising framework for alleviating major cosmological tensions such as the $H_0$ and $S_8$ tensions.

• However, when considered within general relativity, this scenario does not predict any effects on the evolution of the matter density contrast beyond modifications to the background functions.
• In this work, we propose a new gravitational model in which the background dynamics predicted by the $\Lambda_{\rm s}$CDM framework are mapped into $f(T)$ gravity, dubbed $f(T)-\Lambda_{\rm s}$CDM, rendering the models indistinguishable at the background level.
• However, in this new scenario, the sign-switching cosmological constant dynamics modify the evolution of linear matter perturbations through an effective gravitational constant, $G_{\rm eff}$.