Mehdi Assanioussi

Rainbow metric from quantum gravity

Abstract In this Letter, we describe a general mechanism for emergence of a rainbow metric from a quantum cosmological model. This idea is based on QFT on a quantum spacetime. Under general assumptions, we discover that the quantum spacetime on which the field propagates can be replaced by a classical spacetime, whose metric depends explicitly on the energy of the field: as shown by an analysis of dispersion relations, quanta of different energy propagate on different metrics, similar to photons in a refractive material (hence the name “rainbow” used in the literature). In deriving this result, we do not consider any specific theory of quantum gravity: the qualitative behaviour of high-energy particles on quantum spacetime relies only on the assumption that the quantum spacetime is described by a wave-function Ψ o in a Hilbert space H G .

Curvature operator for loop quantum gravity

Loop Quantum Gravity [1] is a promising candidate to finally realize a quantum description of General Relativity. The theory presents two complementary descriptions based on the canonical and the covariant approach (spinfoams) [2]. The first implements the Dirac quantization procedure [3] for GR in Ashtekar-Barbero variables [4] formulated in terms of the so called holonomy-flux algebra [1]: one considers smooth manifolds and on those defines a system of paths and dual surfaces over which connection and electric field can be smeared, and then quantize the system, obtaining the full Hilbert space as the projective limit of the Hilbert space defined on a single graph. The second is instead based on the Plebanski formulation [5] of GR, implemented starting from a simplicial decomposition of the manifold, i.e. restricting to piecewise linear flat geometries. Even if the starting point is different (smooth geometry in the first case, piecewise linear in the second) the two formulations share the same kinematics [6] namely the spin-network basis [7] first introduced by Penrose [8]. In the spinfoam setting then with the help of its piecewise linear nature a beautiful interpretation of the spin-networks in terms of quantum polyhedra [9] naturally arise. This interpretation is not needed in the canonical formalism, where one deals directly with continuous geometries that in the quantum theory result just in polymeric quantum geometries. However in [10] it has been proven that the discrete classical phase space (on a fixed graph) of the canonical approach based on the holonomy-flux algebra can be related to the symplectic reduction of the continuous phase space respect to a flatness constraint; this construction allow then to reconcile the loop gravity geometrical interpretation in terms of singular geometry, and the spin foam interpretation in terms of piecewise flat geometry, since it can be shown that both geometries belong to the same equivalence class. Canonical LQG and Spinfoam appear then much closer if we allow in the first to disentangle the discretization from the quantization procedure. In this article we want to pursue this perspective as a tool to build a curvature operator in LQG, fundamental to solve the most challenging issue in the canonical approach: the quantum dynamics related to the Hamiltonian constraint. The Hamiltonian Constraint has been quantized by Thiemann [11, 12] improving several previous proposals [13] and finally succeeding in defining an anomaly free operator. However this operator is computationally extremely hard to implement and few computations appeared [14, 15] and few solutions have been found [16]. It is defined employing a regularization procedure with specific rules that however might be changed to bring it closer to the spinfoam formalism [17, 18] (till now spoiling the anomaly free property). In particular its Lorentzian part involves several commutators of the extrinsic curvature in order to express the Ricci scalar in terms of Holonomies and Fluxes and this make even the simplest computations extremely hard [19]. However the Lorentzian part of the constraint is just the integral of the Ricci scalar over the 3-dimensional surface of the foliation. The idea developed in this paper is then the following: the Lorentzian term of the Hamiltonian constraint, ∫

Time evolution in deparametrized models of loop quantum gravity

An important aspect in understanding the dynamics in the context of deparametrized models of LQG is to obtain a sufficient control on the quantum evolution generated by a given Hamiltonian operator. More specifically, we need to be able to compute the evolution of relevant physical states and observables with a relatively good precision. In this article, we introduce an approximation method to deal with the physical Hamiltonian operators in deparametrized LQG models, and apply it to models in which a free Klein-Gordon scalar field or a non-rotational dust field is taken as the physical time variable. This method is based on using standard time-independent perturbation theory of quantum mechanics to define a perturbative expansion of the Hamiltonian operator, the small perturbation parameter being determined by the Barbero-Immirzi parameter

Rainbow metric from quantum gravity: Anisotropic cosmology

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Polymer quantization of connection theories: Graph coherent states

. This method allows us to define an approximate spectral decomposition of the Hamiltonian operators and hence to compute the evolution over a certain time interval. As a specific example, we analyze the evolution of expectation values of the volume and curvature operators starting with certain physical initial states, using both the perturbative method and a straightforward expansion of the expectation value in powers of the time variable. This work represents a first step towards achieving the goal of understanding and controlling the new dynamics developed in [25, 26].

Hamiltonian operator for loop quantum gravity coupled to a scalar field

In this paper we present a construction of effective cosmological models which describe the propagation of a massive quantum scalar field on a quantum anisotropic cosmological spacetime. Each obtained effective model is represented by a rainbow metric in which particles of distinct momenta propagate on different classical geometries. Our analysis shows that upon certain assumptions and conditions on the parameters determining such anisotropic models, we surprisingly obtain a unique deformation parameter

New scalar constraint operator for loop quantum gravity

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Emergent de Sitter epoch of the quantum Cosmos

in the modified dispersion relation of the modes. Hence inducing an isotropic deformation despite the general starting considerations. We then ensure the recovery of the dispersion relation realized in the isotropic case, studied in [arXiv:1412.6000], when some proper symmetry constraints are imposed, and we estimate the value of the deformation parameter for this case in loop quantum cosmology context.

Emergent de Sitter Epoch of the Quantum Cosmos from Loop Quantum Cosmology

We present the construction of a new family of coherent states for quantum theories of connections obtained following the polymer quantization. The realization of these coherent states is based on the notion of graph change, in particular the one induced by the quantum dynamics in Yang-Mills and gravity quantum theories. Using a Fock-like canonical structure that we introduce, we derive the new coherent states that we call the graph coherent states. These states take the form of an infinite superposition of basis network states with different graphs. We further discuss the properties of such states and certain extensions of the proposed construction.