Testing a varying-Λ model for dark energy within co-varying physical couplings framework

The Co-varying Physical Couplings (CPC) framework is a modified gravity set up assuming Einstein Field Equations wherein the quantities $\{G,c,\Lambda\}$ are promoted to space-time functions. Bianchi identity and requirement of stress-energy tensor conservation entangle possible variations couplings $\{G,c,\Lambda\}$, which forced co-vary as dictated by General Constraint (GC). In this paper we explore cosmological model $G$, $c$ $\Lambda$ functions redshift respecting GC CPC framework. We assume linear parametrization in terms scale factor $a$. use ansatz $\dot{G}/G = \sigma \left( \dot{c}/c \right)$ with $\sigma =$ constant deduce functional forms $c=c(z)$ $G=G(z)$. show that varying-$\{G,c,\Lambda\}$ fits SNe Ia data $H(z)$ 3$. parameters can be constrained describe dark energy at background level.