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In this paper we consider a third quantized cosmological model with varyingspeed of light $c$ and varying gravitational constant $G$ both represented bynon-minimally coupled scalar fields. The third quantization of such a modelleads to a scenario of the doubleverse with the two components being quantummechanically entangled. We calculate the two parameters describing theentanglement, namely: the energy and the entropy of entanglement where thelatter appears to be a proper measure of the entanglement. We consider apossibility that the entanglement can manifests itself as an effective perfectfluid characterized by the time dependent barotropic index $w_{eff}$, which forsome specific case corresponds to the fluid of cosmic strings. It seems thatsuch an entanglement induced effective perfect fluid may generate significantbackreaction effect at early times.

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