The creation of universes in entangled pairs may avoid the initial singularity and it would have observable consequences in a large macroscopic universe like ours, at least in principle. In this paper we describe the creation of an entangled pair of universes from a double instanton, which avoids the initial singularity, in the case of a homogeneous and isotropic universe with a conformally coupled massless scalar field. The thermodynamical properties of interuniversal entanglement might have observable consequences on the properties of our single universe provided that the thermodynamics of entanglement is eventually related to the classical formulation of thermodynamics. 1. Introduction From the very beginning of human knowledge the creation of the universe has been one of the most exciting, fundamental, and intriguing questions of natural philosophy. In contemporary science, it has been the prime feature of quantum cosmology and it is profoundly related to the existence of space-time singularities and the need of a quantum theory of gravity that would presumably explain or avoid them. In quantum cosmology, the birth of the universe is deeply related to the boundary conditions that we impose on the state of the universe. Different boundary conditions have been proposed in the literature [1–9]. Among them, two main proposals have become customary in quantum cosmology: the Hartle-Hawking no boundary proposal [1, 2, 10] and the Vilenkin tunneling proposal [3, 4, 11]. In both cases, the universe is said to be created from nothing, where by nothing we should not understand the absolute meaning of nothing, that is, something to which we can ascribe no properties, but rather a classically forbidden region of the space-time where space, matter, and above all time do not physically exist as such. The boundary conditions to be imposed on the state of the universe have usually been considered of metaphysical nature and its choice thus a sort of taste. Some particular proposal [5, 12] has claimed to be preferable in order to have a suitable long enough inflationary stage of the universe that would explain the observed homogeneity and isotropy. However, counter-arguments have also been given [13–16]. The main problem for an observational choice of the boundary conditions of the universe is that the rapid expansion of the inflationary period would erase any trace of the preinflationary stage of the universe [12]. Besides, the question would be more unsettled than ever if the results of the Planck mission [17, 18] eventually disfavor typical models of inflation
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