Nonsingular Rotating Black Holes in the Dark-Energy Dominated Universe

Motivated by quantum-gravity scenarios that replace the classical black hole singularity with a regular core, and by the possibility that the dark-energy sector may be scale dependent, we construct a broad class of nonsingular rotating black-hole spacetimes embedded in an improved de Sitter--like background with either constant or running $\Lambda$. Because the Newman--Janis algorithm is generically incompatible with a cosmological-constant fluid, we instead propose a generalized Kerr--Schild construction on a (possibly scale-dependent $\Lambda$) de Sitter seed, yielding a Carter-type metric characterized by a mass function and a $\Lambda$ function. Our construction provides a direct map from static, spherically symmetric regular models to their rotating counterparts. We derive sharp regularity conditions at the ring and we identify a minimal-order subclass. We analyze chronology and show that, for non-negative mass function and $\Lambda$ above a certain negative limit, the spacetimes are stably causal. For minimal-order geometries with non-negative mass, we prove that the weak energy condition must be violated. Finally, we illustrate the framework with an asymptotic-safety--inspired model and discuss horizon structure, surface gravities, and conformal diagrams. These results provide a controlled, observationally oriented arena to confront regular rotating black holes in dark-energy backgrounds with the rapidly improving gravitational-wave and horizon-scale imaging data.