A new perspective on cosmology in Loop Quantum Gravity

Abstract

We present a new cosmological model derived from Loop Quantum Gravity. The formulation is based on a projection of the kinematical Hilbert space of the full theory down to a subspace representing the proper arena for an inhomogeneous Bianchi I model. This procedure gives a direct link between the full theory and its cosmological sector. The emerging quantum cosmological model represents a simplified arena on which the complete canonical quantization program can be tested. The achievements of this analysis could also shed light on Loop Quantum Cosmology and its relation with the full theory.PACS numbers: 04.60. Pp, 98.80.Qc Introduction-A proper quantum description for the gravitational field is expected to avoid the emergence of those singularities which plague General Relativity (GR). In particular, a Quantum Gravity (QG) scenario should tame the initial singularity proper of a homogeneous and eventually isotropic space-time, which does not permit to follow the backward evolution of our Universe before the Big Bang. Therefore, the implementation of a quantum scenario in such symmetry-reduced models gives a privileged arena where the viability of the proposed QG model can be tested.This analysis is particularly useful in the Loop Quantum Gravity (LQG) [1]. This framework provide us with a consistent scheme for the canonical quantization of geometric degrees of freedom. However, it is difficult to extract predictions from LQG, particularly due to the complicated expression of the super-Hamiltonian operator [2, 3] based on the volume operator [4,5] for which no close analytical formulas are available.In symmetry-reduced models the dynamical problem is simplified, thus also the quantum description is expected to be easier with respect to the full theory. Hence, the implementation of LQG in a cosmological space-time could offer a unique opportunity to test the viability of this fundamental description of the gravitational field.A well settled cosmological scenario derived from LQG is described by the theory now called Loop Quantum Cosmology (LQC) [6,7]. In LQC, one first reduces the phase-space according with the symmetries of a homogeneous space-time and then quantize using LQG techniques. However it has not yet been shown that the cos-

Homogeneous cosmologies as group field theory condensates

“…For instance, in similar contexts in discrete geometry one often thinks of cubical graphs, where the elementary cell is a "cube" that can be thought of as composed of several tetrahedra. Most notably, recent work in loop quantum gravity [47,48] aims at deriving cosmological dynamics from LQG using cubulations of space. A condensate of cubes would represent the closest analogue to such a construction in our setting, and could be used to compare our approach with the work of [47,48] in more detail.…”

Curvature operator for loop quantum gravity

“…Our hope is that the curvature operator we built will allow us to construct a more analytically manageable Hamiltonian operator and will give the possibility to construct solutions in order to get more insights on the dynamical sector of LQG both in the full theory [43,44] and in simplified models [45][46][47][48]. This will be the subject of upcoming works.…”

Loop Quantum Cosmology, Modified Gravity and Extra Dimensions

“…It should be mentioned that, because of length limitation, many aspects of LQC are not covered. These topics include but are not limited to inflationary scenarios in LQC [57], Starobinski types model [58,59], the value of Immirzi parameters in higher dimensions [60], linking LQC with LQG [61,62], more detailed discussion on singularity issues [63,64], and so on.…”