arXiv subjects

Emanuele Alesci

Publications and source records attributed to Emanuele Alesci.

At least 19 recordsLinked to original sources

arXiv2023

Graphical calculus of spin networks

Graphical techniques provide a very useful practical device for calculations involving the so-called spin network states, which encode the quantum degrees of freedom of spatial geometry in loop quantum gravity. Graphical calculus of SU(2), which has been originally introduced in the literature in order to deal with calculations arising from the coupling of angular momenta in quantum mechanics, can be used as a simple but powerful method for computing the action of various physically interesting operators in the spin network representation. Compared with conventional manipulation of algebraic expressions, calculations in the graphical approach are typically more convenient, concise and visually transparent. The goal of this chapter is to provide an accessible introduction to graphical methods in SU(2) recoupling theory and a brief description of their use as a tool for practical calculations in loop quantum gravity. We introduce the basics of the graphical formalism, and establish the representation of the elementary states and operators of loop quantum gravity in graphical form. Several example calculations are given to illustrate the use of the graphical techniques, including a computation of the matrix elements of a Hamiltonian constraint operator in the spin network basis.

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arXiv2022

Understanding quantum black holes from quantum reduced loop gravity

We systematically study the top-down model of loop quantum black holes (LQBHs), recently derived by Alesci, Bahrami and Pranzetti (ABP). To understand the structure of the model, we first derive several well-known LQBH solutions by taking proper limits. These include the Böhmer-Vandersloot and Ashtekar-Olmedo-Singh models, which were all obtained by the so-called bottom-up polymerizations within the framework of the minisuperspace quantizations. Then, we study the ABP model, and find that the inverse volume corrections become important only when the radius of the two-sphere is of the Planck size. For macroscopic black holes, the minimal radius obtained at the transition surface is always much larger than the Planck scale, and hence these corrections are always sub-leading. The transition surface divides the whole spacetime into two regions, and in one of them the spacetime is asymptotically Schwarzschild-like, while in the other region, the asymptotical behavior sensitively depends on the ratio of two spin numbers involved in the model, and can be divided into three different classes. In one class, the spacetime in the 2-planes orthogonal to the two spheres is asymptotically flat, and in the second one it is not even conformally flat, while in the third one it can be asymptotically conformally flat by properly choosing the free parameters of the model. In the latter, it is asymptotically de Sitter. However, in any of these three classes, sharply in contrast to the models obtained by the bottom-up approach, the spacetime is already geodesically complete, and no additional extensions are needed in both sides of the transition surface. In particular, identical multiple black hole and white hole structures do not exist.

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arXiv2020

Asymptotically de Sitter Universe inside a Schwarzschild black hole

Extending our previous analysis, we study the interior of a Schwarzschild black hole derived from a partial gauge fixing of the full Loop Quantum Gravity Hilbert space, this time including the inverse volume and coherent state subleading corrections. Our derived effective Hamiltonian differs crucially from the ones introduced in the minisuperspace models. This distinction is reflected in the class of homogeneous bouncing geometries that replace the classical singularity and are labeled by a set of quantum parameters associated with the structure of coherent states used to derive the effective Hamiltonian. By fixing these quantum parameters through geometrical considerations, the post-bounce interior geometry reveals a high sensitivity to the value of the Barbero-Immirzi parameter $γ$. Surprisingly, we find that $γ\approx 0.274$ results in an asymptotically de Sitter geometry in the interior region, where now a cosmological constant is generated purely from quantum gravitational effects. The striking fact is the exact coincidence of this value for $γ$ with the one derived from the SU(2) black hole entropy calculations in Loop Quantum Gravity. The emergence of this value in two entirely unrelated theoretical frameworks and computational setups is strongly suggestive of deep ties between the area gap in Loop Quantum Gravity, black hole physics, and the observable Universe. In connection to the latter, we point out an intriguing relation between the measured value of the cosmological constant and the observed mass in the Universe from a proposal for a spin quantum number renormalization effect associated to the microscopic dynamics.

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arXiv2019

Quantum gravity predictions for black hole interior geometry

In a previous work we derived an effective Hamiltonian constraint for the Schwarzschild geometry starting from the full loop quantum gravity Hamiltonian constraint and computing its expectation value on coherent states sharply peaked around a spherically symmetric geometry. We now use this effective Hamiltonian to study the interior region of a Schwarzschild black hole, where a homogeneous foliation is available. Descending from the full theory, our effective Hamiltonian, though still bearing the well known ambiguities of the quantum Hamiltonian operator, preserves all relevant information about the fundamental discreteness of quantum space. This allows us to have a uniform treatment for all quantum gravity holonomy corrections to spatially homogeneous geometries, unlike the minisuperspace loop quantization models in which the effective Hamiltonian is postulated. We show how, for several geometrically and physically well motivated choices of coherent states, the classical black hole singularity is replaced by a homogeneous expanding Universe. The resultant geometries have no significant deviations from the classical Schwarzschild geometry in the pre-bounce sub-Planckian curvature regime, evidencing the fact that large quantum effects are avoided in these models. In all cases, we find no evidence of a white hole horizon formation. However, various aspects of the post-bounce effective geometry depend on the choice of quantum states.

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arXiv2019

Quantum evolution of black hole initial data sets: Foundations

We construct a formalism for evolving spherically symmetric black hole initial data sets within a canonical approach to quantum gravity. This problem can be formulated precisely in quantum reduced loop gravity, a framework which has been successfully applied to give a full theory derivation of loop quantum cosmology. We extend this setting by implementing a particular choice of partial gauge which is then used to select a kinematical Hilbert space where the symmetry reduction is imposed through semiclassical states. The main result of this investigation is an effective Hamiltonian that can be used to solve for quantum black hole geometries by evolving classical black hole initial data sets.

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arXiv2019

Quantum reduced loop gravity effective Hamiltonians from a statistical regularization scheme

We introduce a new regularization scheme for Quantum Cosmology in Loop Quantum Gravity (LQG) using the tools of Quantum Reduced Loop Gravity (QRLG). It is obtained considering density matrices for superposition of graphs based on statistical countings of microstates compatible with macroscopic configurations. We call this procedure statistical regularization scheme. In particular, we show how the $μ_0$ and $\barμ$ schemes introduced in Loop Quantum Cosmology (LQC) emerge with specific choices of density matrices. Within this new scheme we compute effective Hamiltonians suitable to describe quantum corrected Friedmann and Bianchi I universes and their leading orders coincide with the corresponding effective LQC Hamiltonians in the $\barμ$ scheme. We compute the next to the leading orders corrections and numerical investigation of the resulting dynamics shows evidence for the emergent-bouncing universe scenario to be a general property of the isotropic sector of QRLG.

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arXiv2019

Bianchi I effective dynamics in Quantum Reduced Loop Gravity

The effective quantum dynamics of Bianchi I spacetime is addressed within the statistical regularization scheme in Quantum Reduced Loop Gravity. The case of a minimally coupled massless scalar field is studied and compared with the effective $\barμ-$Loop Quantum Cosmology. The dynamics provided by the two approaches match in the semiclassical limit but differ significantly after the bounces. Analytical and numerical inspections show that energy density, expansion scalar and shear are bounded also in Quantum Reduced Loop Gravity and the classical singularity is resolved for generic initial conditions in all spatial directions.

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arXiv2018

Phenomenology of Quantum Reduced Loop Gravity in the isotropic cosmological sector

Quantum reduced loop gravity is designed to consistently study symmetry reduced systems within the loop quantum gravity framework. In particular, it bridges the gap between the effective cosmological models of loop quantum cosmology and the full theory, addressing the dynamics before the minisuperspace reduction. This mostly preserves the graph structure and SU(2) quantum numbers. In this article, we study the phenomenological consequences of the isotropic sector of the theory, the so-called emergent bouncing universe model. In particular, the parameter space is scanned and we show that the number of inflationary e-folds is almost always higher than the observational lower-bound. We also compute the primordial tensor power spectrum and study its sensitivity upon the fundamental parameters used in the model.

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arXiv2018

Power spectrum of primordial perturbations for an emergent universe in quantum reduced loop gravity

We study the dynamics and predictions of a new emergent-universe model recently derived within Quantum Reduced Loop Gravity and based on the so-called statistical regularization scheme. These effective geometries show a dynamical transition from a stationary spacetime, with nearly constant scale factor at very early times, to a late-time semiclassical phase well approximated by a classical Friedmann-Robertson-Walker spacetime. We show that this is always the case when the matter content is a minimally coupled scalar field subject to a quadratic potential, including the massless case. Besides, a finite period of (nearly) exponential expansion in the semiclassical region can take place. Hence, we incorporate cosmological scalar and tensor perturbations, with a well-defined dynamics, and compute their power spectra at the end of inflation. We show that they are nearly scale invariant up to some scale where scale invariance is broken. Besides, they show qualitative differences with respect to the bouncing scenario of Loop Quantum Cosmology at scales where the scale invariance is broken. Nevertheless, the tensor-to-scalar ratio remains approximately constant even for modes well affected by the background evolution.

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arXiv2018

Orthogonal gauge fixing of first order gravity

We consider the first order connection formulation of 4D general relativity in the "orthogonal" gauge. We show how the partial gauge fixing of the phase space canonical coordinates leads to the appearance of second class constraints in the theory. We employ the gauge unfixing procedure in order to successfully complete the Dirac treatment of the system. While equivalent to the inversion of the Dirac matrix, the gauge unfixing allows us to work directly with the reduced phase space and the ordinary Poisson bracket. At the same time, we explicitly derive the new set of residual first class constraints preserving the partial gauge fixing, which are linear combinations of the original constraints, and these turn out to contain nonlinear terms. While providing an explicit example of how to consistently recast general relativity in a given partial gauge, the main motivation of this classical analysis is the application of the Quantum Reduced Loop Gravity program to a Schwarzschild black hole geometry.

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arXiv2017

Cosmological singularity resolution from quantum gravity: the emergent-bouncing universe

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 "emergent-bouncing 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.

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arXiv2016

Quantum reduced loop gravity: extension to gauge vector field

Within the framework of Quantum Reduced Loop Gravity we quantize the Hamiltonian for a gauge vector field. The regularization can be performed using tools analogous to the ones adopted in full Loop Quantum Gravity, while the matrix elements of the resulting operator between basis states are analytic coefficients. This analysis is the first step towards deriving the full quantum gravity corrections to the vector field semiclassical dynamics.

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arXiv2016

Coherent 3j-symbol representation for the loop quantum gravity intertwiner space

We introduce a new technique for dealing with the matrix elements of the Hamiltonian operator in loop quantum gravity, based on the use of intertwiners projected on coherent states of angular momentum. We give explicit expressions for the projections of intertwiners on the spin coherent states in terms of complex numbers describing the unit vectors which label the coherent states. Operators such as the Hamiltonian can then be reformulated as differential operators acting on polynomials of these complex numbers. This makes it possible to describe the action of the Hamiltonian geometrically, in terms of the unit vectors originating from the angular momentum coherent states, and opens up a way towards investigating the semiclassical limit of the dynamics via asymptotic approximation methods.

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arXiv2016

Quantum Reduced Loop Gravity and the foundation of Loop Quantum Cosmology

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.

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arXiv2016

Improved regularization from Quantum Reduced Loop Gravity

The choice of the regularization scheme in Loop Quantum Cosmology (LQC) is crucial for the predicted phenomenology. We outline how the improved scheme can be naturally realized in Quantum Reduced Loop Gravity, describing the Universe as an ensemble of microstates labeled by different graphs. The new effective dynamics presents corrections to LQC, which do not significantly affect the bouncing scenario for the most relevant kinds of matter fields in cosmology $(w \leq 1)$.

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arXiv2015

Coherent State Operators in Loop Quantum Gravity

We present a new method for constructing operators in loop quantum gravity. The construction is an application of the general idea of "coherent state quantization", which allows one to associate a unique quantum operator to every function on a classical phase space. Using the heat kernel coherent states of Hall and Thiemann, we show how to construct operators corresponding to functions depending on holonomies and fluxes associated to a fixed graph. We construct the coherent state versions of the fundamental holonomy and flux operators, as well as the basic geometric operators of area, angle and volume. Our calculations show that the corresponding canonical operators are recovered from the coherent state operators in the limit of large spins.

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arXiv2015

Quantum reduced loop gravity: extension to scalar field

The quantization of the Hamiltonian for a scalar field is performed in the framework of Quantum Reduced Loop Gravity. We outline how the regularization can be performed by using the analogous tools adopted in full Loop Quantum Gravity and the matrix elements of the resulting operator between basis states are analytic coefficients. These achievements open the way for a consistent analysis of the Quantum Gravity corrections to the classical dynamics of gravity in the presence of a scalar field in a cosmological setting.

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arXiv2015

Quantum Reduced Loop Gravity: a realistic Universe

We describe the quantum flat universe in QRLG in terms of states based at cuboidal graphs with six-valent nodes. We investigate the action of the scalar constraint operator at each node and we construct proper semiclassical states. This allows us to discuss the semiclassical effective dynamics of the quantum universe, which resembles that of LQC. In particular, the regulator is identified with the third root of the inverse number of nodes within each homogeneous patch, while inverse-volume corrections are enhanced.

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