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Register a new userDoubleverse entanglement in third quantized non-minimally coupled varying constants cosmologies
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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 $w_{eff}$, 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.
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We consider gravity theory with varying speed of light and varying gravitational constant. Both constants are represented by non-minimally coupled scalar fields. We examine the cosmological evolution in the near curvature singularity regime. We find that at the curvature singularity the speed of light goes to infinity while the gravitational constant vanishes. This corresponds to the Newtons Mechanics limit represented by one of the vertex of the Bronshtein-Zelmanov-Okun cube. The cosmological evolution includes both the pre-big-bang and post-big-bang phases separated by the curvature singularity. We also investigate the quantum counterpart of the considered theory and find the probability of transition of the universe from the collapsing pre-big-bang phase to the expanding post-big-bang phase.
Although the standard cosmological model explains most of the observed phenomena it still struggles with the problem of initial singularity. An interesting scenario in which the problem of the initial singularity is somehow circumvented was proposed in the context of string theory where the canonical quantisation procedure was additionally applied. A similar effect can be achieved in the context of the canonically quantized theory with varying speed of light and varying gravitational constant where both quantities are represented by non-minimally coupled scalar fields. Such theory contains both the pre-big-bang contracting phase and the post-big-bang expanding phase and predicts non-vanishing probability of the transition from the former to the latter phase. In this paper we quantize such a theory once again by applying the third quantization scheme and show that the resulting theory contains scenario in which the whole multiverse is created from nothing. The generated family of the universes is described by the Bose-Einstein distribution.
Recent works showing that homogeneous and isotropic cosmologies involving scalar fields correspond to geodesics of certain augmented spaces are generalized to the non-minimal coupling case. As the Maupertuis-Jacobi principle in classical mechanics, this result allows us, in principle, to infer some of the dynamical properties of the cosmologies from the geometry of the associated augmented spaces.
In this paper we discuss local averages of the energy density for the non-minimally coupled scalar quantum field, extending a previous investigation of the classical field. By an explicit example, we show that such averages are unbounded from below on the class of Hadamard states. This contrasts with the minimally coupled field, which obeys a state-independent lower bound known as a Quantum Energy Inequality (QEI). Nonetheless, we derive a generalised QEI for the non-minimally coupled scalar field, in which the lower bound is permitted to be state-dependent. This result applies to general globally hyperbolic curved spacetimes for coupling constants in the range $0<xileq 1/4$. We analyse the state-dependence of our QEI in four-dimensional Minkowski space and show that it is a nontrivial restriction on the averaged energy density in the sense that the lower bound is of lower order, in energetic terms, than the averaged energy density itself.
The paper deals with a non--minimally coupled scalar field in the background of homogeneous but anisotropic Kantowski--Sachs space--time model. The form of the coupling function of the scalar field with gravity and the potential function of the scalar field are not assumed phenomenologically, rather they are evaluated by imposing Noether symmetry to the Lagrangian of the present physical system. The physical system gets considerable mathematical simplification by a suitable transformation of the augmented variables $(a, b, phi)rightarrow (u, v, w)$ and by the use of the conserved quantities due to the geometrical symmetry. Finally, cosmological solutions are evaluated and analyzed from the point of view of the present evolution of the Universe.
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