Cosmological perturbations in the entangled inflationary universe

In this paper it is presented the model of a multiverse made up of universes which are created in entangled pairs that conserve the total momentum conjugated to the scale factor. For the background spacetime it is assumed a FRW metric with a scalar field with mass $m$ minimally coupled to gravity. For the fields that propagate in the entangled spacetimes it is considered the perturbations of the spacetime and the scalar field, whose quantum states become entangled too. They turn out to be in a quasi thermal state and the corresponding thermodynamical magnitudes are computed. Three observables are expected to be caused by the creation of the universes in entangled pairs: a modification of the Friedmann equation because the entanglement of the spacetimes, a modification of the effective value of the potential of the scalar field by the backreaction of the perturbation modes, and a modification of the spectrum of fluctuations because the thermal distribution induced by the entanglement of the partner universes. The later would be a distinctive feature of the creation of universes in entangled pairs.