Doubleverse entanglement in third quantized non-minimally coupled varying constants cosmologies

In this paper we consider a third quantized cosmological model with varying speed of light c and varying gravitational constant G both represented by non-minimally coupled scalar fields. The third quantization of such a model leads to a scenario of the doubleverse with the two components being quantum mechanically entangled. We calculate the two parameters describing the entanglement, namely: the energy and the entropy of entanglement where the latter appears to be a proper measure of the entanglement. We consider a possibility that the entanglement can manifests itself as an effective perfect fluid characterized by the time dependent barotropic index weff, which for some specific case corresponds to the fluid of cosmic strings. It seems that such an entanglement induced effective perfect fluid may generate significant backreaction effect at early times.