We have successfully integrated Lambda(s) Cold Dark Matter (CDM), a promising scenario for alleviating major cosmological tensions, into a concrete theoretical framework by endowing it with a specific Lagrangian from the VCDM model, a type-II minimally modified gravity. This promotes the scenario to a fully predictive model (dubbed Lambda(s) VCDM) that specifies the cosmological evolution self-consistently, including through the late-time anti-de Sitter (AdS)to-de Sitter (dS) transition epoch. In this theory, an auxiliary scalar field generates an effective cosmological constant in the Friedmann equation not only when endowed with a constant potential, but also when endowed with a linear potential. This property allows an abrupt mirror AdS-to-dS transition to be realized via a piecewise-linear potential, implemented as a sudden change in slope at a junction. To remove the associated sudden (type-II) singularity and ensure stable evolution, we smooth the junction using a blended sigmoid interpolant, obtaining rapid but continuous transitions. We identify two qualitatively distinct smooth mirror AdS-todS realizations of Lambda(s): (i) an agitated transition, in which the potential interpolates between equal-magnitude AdS and dS plateaus and Lambda(s) generically develops a central bump; and (ii) a quiescent transition, in which the potential remains continuous but changes slope across the transition layer, so that Lambda(s)(a) can remain monotone (possibly with shallow entrance/exit shoulders) and a central bump is not automatic. Depending on the transition type and sharpness, a finite-width transition can induce a transient accelerated-expansion interval ( a > 0) around the transition redshift ( z similar to 1 . 5-2), in addition to the present-day accelerated expansion (for z approximate to 0.6 as in Lambda CDM), and, if the background enters aregion where V ,(phi phi)> 2 / 3, a nested super-acceleration (H-center dot > 0) episode (and hence a bump in H ). These distinct transient expansion histories can imprint characteristic signatures on both background and perturbation evolution; while the linear perturbation system is, in form, identical to that of Lambda CDM, the scalar sector is modified through a H-center dot-dependent relation, with deviations localized primarily to the transition epoch. Our construction therefore enables a self-consistent observational assessment of smooth Lambda sCDM realizations and motivates dedicated multiprobe analyses to test transition dynamics and reassess cosmological tensions. Further work is warranted to assess whether Lambda(s)CDMcan emerge as a credible extension of the concordance model, or at least as a useful guide for exploring its potential revisions.
Akarsu et al. (Thu,) studied this question.