Researchers propose a bimetric cosmological model where fundamental constants, such as the gravitational constant G and the propagation speed of gravitational interactions c_grav, vary dynamically with time. In this framework, the gravitational and matter sectors are described by distinct metrics, linked by a time-dependent function α(t). This relation implies that G(t) is proportional to α^(-3) and c_grav(t) is proportional to α^(-1).

The study focuses on a class of solutions where α tends to infinity at a finite cosmic time, which in turn causes G and c_grav to tend to zero. For an analytically tractable solution, it is shown that this final singularity occurs at a finite conformal time and possesses a conformal structure compatible with a possible transition between successive cosmological cycles. The Tipler and Królak criteria confirm that this singularity is strong.

The physical consequences of this weakening gravitational interaction are significant. They include the dissolution of gravitationally bound structures and the shrinking of black-hole horizons. These effects suggest a possible mechanism leading towards an effectively radiation-dominated final state, a scenario relevant for Conformal Cyclic Cosmology. The results motivate the extension of this analysis to more general scalar-tensor theories of gravity.