We introduce a new framework for loop quantum gravity: mimicking the spinfoam quantization procedure we propose to study the symmetric sectors of the theory imposing the reduction weakly on the full kinematical Hilbert space of the canonical theory. As a first application of Quantum-Reduced Loop Gravity we study the inhomogeneous Bianchi I model. 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 elucidate the relationship between Loop Quantum Cosmology and the full theory.

Alternative scenarios to the Big Bang singularity have been subject of intense research for several decades by now. Most popular in this sense have been frameworks were such singularity is replaced by a bounce around some minimal cosmological volume or by some early quantum phase. This latter scenario was devised a long time ago and referred as an "emergent universe" (in the sense that our universe emerged from a constant volume quantum phase). We show here that within an improved framework of canonical quantum gravity (the so called Quantum Reduced Loop Gravity) the Friedmann equations for cosmology are modified in such a way to replace the big bang singularity with a short bounce preceded by a metastable quantum phase in which the volume of the universe oscillates between a series of local maxima and minima. We call this hybrid scenario an "emergentbouncing universe" since after a pure oscillating quantum phase the classical Friedmann spacetime emerges. Perspective developments and possible tests of this scenario are discussed in the end.

We discuss the semiclassical limit of Quantum Reduced Loop Gravity, a recently proposed model to address the quantum dynamics of the early Universe. We apply the techniques developed in full Loop Quantum Gravity to define the semiclassical states in the kinematical Hilbert space and evaluating the expectation value of the euclidean scalar constraint we demonstrate that it coincides with the classical expression, i.e. the one of a local Bianchi I dynamics. The result holds as a leading order expansion in the scale factors of the Universe and opens the way to study the subleading corrections to the semiclassical dynamics. We outline how by retaining a suitable finite coordinate length for holonomies our effective Hamiltonian at the leading order coincides with the one expected from LQC. This result is an important step in fixing the correspondence between LQG and LQC.

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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-

The Hamiltonian formulation of the Holst action is reviewed and it is provided a solution of secondclass constraints corresponding to a generic local Lorentz frame. Within this scheme the form of rotation constraints can be reduced to a Gauss-like one by a proper generalization of AshtekarBarbero-Immirzi connections. This result emphasizes that the Loop Quantum Gravity quantization procedure can be applied when the time-gauge condition does not stand.

We show how Loop Quantum Cosmology can be derived as an effective semiclassical description of Loop Quantum Gravity. Using the tools of QRLG, a gauge fixed version of LQG, we take the coherent states of the fundamental microscopic theory suitable to describe a Bianchi I Universe and we find a mapping between the expectation value of the Hamiltonian and the dynamics of LQC. Our results are in agreement with a lattice refinement framework for LQC, thus the so called "old" and "improved-dynamics" regularization schemes can be reproduced. These amount to different choices of relations between local variables and the smeared ones entering the definition of the coherent states. The leading order of the fundamental theory corresponds to LQC, but we also find different inverse volume corrections, that depend on a purely quantum observable, namely the number of nodes of the states. PACS numbers: 04.60.PpThe attempts towards a quantum theory for the gravitational field encountered several interpretative and conceptual issues. The latter are partially tamed in a cosmological setting, in which some degrees of freedom are frozen and the dynamic problem simplifies. This is the case already for the Wheeler-DeWitt framework, whose implementation in minisuperspace [1] allows to go further in the quantization procedure, even though no new achievement in the characterization of a Quantum Universe is obtained (no removal of singularity or of chaotic behavior for Bianchi IX model). On the contrary, in Loop Quantum Cosmology (LQC) [2-4] a viable description for the early Universe is provided: the initial singularity is generically replaced by a Big-Bounce [5], while there are some indications that the chaotic structure of the Bianchi IX solution is tamed [6].The investigation of the phenomenological implications of LQC [7,8] (see [9] for a review) opens up the possibility to validate the theory in a nearby future in view of the continuous progress of experimental cosmology (CMB power spectrum and polarization, neutrino cosmology, gravitational waves detection). This validation would not only give us a detailed knowledge of the Universe early phases, but it could also enhance our comprehension of fundamental fields at the Planck scale, given the expected link between LQC and Loop Quantum Gravity (LQG) [10]. In fact, LQC aims to provide the cosmological sector of LQG, but till now no direct derivation of the former from the latter has been given.In this work, we bridge the two theories. The intermediate step we use is Quantum-Reduced-Loop-Gravity (QRLG) [11][12][13], which is realized by imposing some gauge-fixing conditions weakly in the kinematical Hilbert space of LQG. These gauge-fixing conditions restrict the full Hilbert space to one describing a diagonal metric tensor and diagonal (inverse) drei-bein fields. This formulation has the merit to preserve a (cuboidal) graph structure with SU(2) quantum numbers at links and intertwiners at nodes, thus accounting for the main features of LQG in a simplified context.The dynamics of the r...

Quantum Reduced Loop Gravity is a promising framework for linking Loop Quantum Gravity and the effective semiclassical dynamics of Loop Quantum Cosmology. We review its basic achievements and its main perspectives, outlining how it provides a quantum description of the Universe in terms of a cuboidal graph which constitutes the proper framework for applying loop techniques in a cosmological setting.