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Register a new userGeneralized quantum gravity condensates for homogeneous geometries and cosmology
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We construct a generalized class of quantum gravity condensate states, that allows the description of continuum homogeneous quantum geometries within the full theory. They are based on similar ideas already applied to extract effective cosmological dynamics from the group field theory formalism, and thus also from loop quantum gravity. However, they represent an improvement over the simplest condensates used in the literature, in that they are defined by an infinite superposition of graph-based states encoding in a precise way the topology of the spatial manifold. The construction is based on the definition of refinement operators on spin network states, written in a second quantized language. The construction lends itself easily to be applied also to the case of spherically symmetric quantum geometries.
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Quantum gravity aims to describe gravity in quantum mechanical terms. How exactly this needs to be done remains an open question. Various proposals have been put on the table, such as canonical quantum gravity, loop quantum gravity, string theory, etc. These proposals often encounter technical and conceptual problems. In this chapter, we focus on canonical quantum gravity and discuss how many conceptual problems, such as the measurement problem and the problem of time, can be overcome by adopting a Bohmian point of view. In a Bohmian theory (also called pilot-wave theory or de Broglie-Bohm theory, after its originators de Broglie and Bohm), a system is described by certain variables in space-time such as particles or fields or something else, whose dynamics depends on the wave function. In the context of quantum gravity, these variables are a space-time metric and suitable variable for the matter fields (e.g., particles or fields). In addition to solving the conceptual problems, the Bohmian approach yields new applications and predictions in quantum cosmology. These include space-time singularity resolution, new types of semi-classical approximations to quantum gravity, and approximations for quantum perturbations moving in a quantum background.
This is the second paper in a series of four in which we use space adiabatic methods in order to incorporate backreactions among the homogeneous and between the homogeneous and inhomogeneous degrees of freedom in quantum cosmological perturbation theory. The purpose of the present paper is twofold. On the one hand, it illustrates the formalism of space adiabatic perturbation theory (SAPT) for two simple quantum mechanical toy models. On the other, it proves the main point, namely that backreactions lead to additional correction terms in effective Hamiltonians that one would otherwise neglect in a crude Born-Oppenheimer approximation. The first model that we consider is a harmonic oscillator coupled to an anharmonic oscillator. We chose it because it displays many similarities with the more interesting second model describing the coupling between an inflaton and gravity restricted to the purely homogeneous and isotropic sector. These results have potential phenomenological consequences in particular for quantum cosmological theories describing big bounces such as Loop Quantum Cosmology (LQC).
I will briefly discuss three cosmological models built upon three distinct quantum gravity proposals. I will first highlight the cosmological role of a vector field in the framework of a string/brane cosmological model. I will then present the resolution of the big bang singularity and the occurrence of an early era of accelerated expansion of a geometric origin, in the framework of group field theory condensate cosmology. I will then summarise results from an extended gravitational model based on non-commutative spectral geometry, a model that offers a purely geometric explanation for the standard model of particle physics.
We introduce three families of classical and quantum solutions to the leading order of string effective action on spatially homogeneous $(2+1)$-dimensional space-times with the sources given by the contributions of dilaton, antisymmetric gauge $B$-field, and central charge deficit term $Lambda$. At the quantum level, solutions of Wheeler-DeWitt equations have been enriched by considering the quant
The goal of this paper is to employ a preclusion principle originally suggested by Rafael Sorkin in order to come up with a relativistically covariant model of quantum mechanics and gravity. Space-time is viewed as geometry as opposed to dynamics, and unwanted histories in that geometry are precluded.
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