Quantum-reduced loop gravity is a model of loop quantum gravity, which - from the technical point of view - is characterized by the remarkably simple form of its basic operators. In this article we examine the operators of the quantum-reduced model from the perspective of full loop quantum gravity. We show that, in spite of their simplicity, the operators of the quantum-reduced model are simply the operators of the full theory acting on states in the Hilbert space of the quantum-reduced model. The passage from the full theory operators to the "reduced" operators simply consists of noting that the states of the quantum-reduced model are assumed to carry large spin quantum numbers, and discarding terms which are of lower than leading order in $j$. Our findings clarify the relation between the quantum-reduced model and full loop quantum gravity, and strengthen the technical foundations on which the kinematical structure of the quantum-reduced model is based.
The perspective is advanced that the time parameter in quantum mechanics corresponds to the time coordinate in a Minkowski flat spacetime local approximation to the actual dynamical curved spacetime of General Relativity, rather than to an external Newtonian reference frame. There is no incompatibility, as generally assumed in the extensively discussed "problem of time" in Quantum Gravity.
The idea that quantum gravity manifestations would be associated with a violation of Lorentz invariance is very strongly bounded and faces serious theoretical challenges. Other related ideas seem to be drowning in interpretational quagmires. This leads us to consider alternative lines of thought for such phenomenological search. We discuss the underlying viewpoints and briefly mention their possible connections with other current theoretical ideas.
In this paper we demonstrate closure of the quantum algebra of Hamiltonian constraints in a theory directly related to a certain sector of general relativity reduced to diagonal variables.
The quantum-reduced loop-gravity technique has been introduced for dealing with cosmological models. We show that it can be applied rather generically: anytime the spatial metric can be gauge-fixed to a diagonal form. The technique selects states based on reduced graphs with Livine-Speziale coherent intertwiners and could simplify the analysis of the dynamics in the full theory.
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.
Gravity is one of the most inexplicable forces of nature, controlling everything, from the expansion of the Universe to the ebb and flow of ocean tides. The search for the laws of motion and gravitation began more than two thousand years ago but still we do not have the complete picture of it. In this article, we have outlined how our understanding of gravity is changing drastically with time and how the previous explanations have shaped the most recent developments in the field like superstrings and braneworlds.
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.
We solve perturbative constraints and eliminate gauge freedom for Ashtekar's gravity on de Sitter background. We show that the reduced phase space consists of transverse, traceless, symmetric fluctuations of the triad and of transverse, traceless, symmetric fluctuations of the connection. A part of gauge freedom corresponding to the conformal Killing vectors of the three-manifold can be fixed only by imposing conditions on Lagrange multiplier. The reduced phase space is equivalent to that of ADM gravity on the same background.
In the context of canonical quantum gravity, we study an alternative real quantisation scheme, which is arising by relating simpler Riemannian quantum theory to the more complicated physical Lorentzian theory - the generalised Wick transform. On the symmetry reduced models, homogenous Bianchi cosmology and 2+1 gravity, we investigate its generalised construction principle, demonstrate that the emerging quantum theory is equivalent to the one obtained from standard quantisation and how to obtain physical states in Lorentzian gravity from Wick transforming solutions of Riemannian quantum theory.
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.
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 $(w \leq 1)$.
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 cond…
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 th…
Sakharov's 1967 notion of ``induced gravity'' is currently enjoying a significant resurgence. The basic idea, originally presented in a very brief 3-page paper with a total of 4 formulas, is that gravity is not ``fundamental'' in the sense of particle physics. Instead it was argued that gravity (general relativity) emerges from quantum field theory in roughly the same sense that hydrodynamics or continuum elasticity theory emerges from molecular physics. In this article I will translate the key ideas into modern language, and explain the various versions of Sakharov's idea currently on the mar…
The relation between the SL(2,R)/SO(2)- and the SL(2,C)-chiral model that naturally arise within the metric respectively the Ashtekar formulation of two Killing field reduced Einstein gravity is revealed. Both chiral models turn out to be completely equivalent even though the transition from the coset- to the SL(2,C)-model is accompanied by a disappearance of the non-ultralocal terms in the Poisson brackets.
Quantum Reduced Loop Gravity provides a promising framework for a consistent characterization of the early Universe dynamics. Inspired by BKL conjecture, a flat Universe is described as a collection of Bianchi I homogeneous patches. The resulting quantum dynamics is described by the scalar constraint operator, whose matrix elements can be analytically computed. The effective semiclassical dynamics is discussed, and the differences with Loop Quantum Cosmology are emphasized.
Introducing a new method, we demonstrate how the action of reduced operators can be derived without resorting to a recoupling theory and how they exactly reproduce the results obtained in the standard approach of Quantum Reduced Loop Gravity (QRLG). This is particularly relevant while dealing with volume operator when dealing with the coupling of matter fields to gravity. Apart from reinforcing the close link between QRLG and loop quantum cosmology (LQC), this procedure also sheds new light on the issue of how to extract the continuum limit, without resorting to the large-$j$ expansion, thereb…
We study the phase space of the spherically symmetric solutions of the system obtained from the dimensional reduction of the six-dimensional Einstein-Gauss-Bonnet action with a cosmological constant. We show that all the physical solutions have anti-de Sitter asymptotic behavior.
We study the phase space of the spherically symmetric solutions of the system obtained from the dimensional reduction of the six-dimensional Einstein-Gauss- Bonnet action. We show the existence of solutions with nonflat asymptotic behavior.
We obtain two dimensional analogue of the Jordan-Brans-Dicke (JBD) gravity action described in four dimensional spherically symmetric curved space time metric. There will be two scalar fields, namely, the Brans Dicke (BD) $ϕ$ and scale factor of 2-sphere part of the space time $ψ.$ We obtained suitable duality transformations between $(ψ,ϕ)$ and $(ρ,S)$ where $ρ$ and $S$ is respectively amplitude and phase part of the corresponding de Broglie pilot wave function $Ψ(ρ,S)=\sqrtρe^{iS}.$ Covariant conservation of mass-energy current density of particles ensemble $J_a=ρ\partial_aS,$ is established…
We study some two-dimensional dilaton gravity models using the formal theory of partial differential equations. This allows us to prove that the reduced phase space is two-dimensional without an explicit construction. By using a convenient (static) gauge we reduce the theory to coupled \ode s and we are able to derive for some potentials of interest closed-form solutions. We use an effective (particle) Lagrangian for the reduced field equations in order to quantize the system in a finite-dimensional setting leading to an exact partial differential Wheeler-DeWitt equation instead of a functiona…
I give a brief overview of some Quantum-Gravity-Phenomenology research lines, focusing on studies of cosmic rays and gamma-ray bursts that concern the fate of Lorentz symmetry in quantum spacetime. I also stress that the most valuable phenomenological analyses should not mix too many conjectured new features of quantum spacetime, and from this perspective it appears that it should be difficult to obtain reliable guidance on the quantum-gravity problem from the analysis of synchrotron radiation from the Crab nebula and from the analysis of phase coherence of light from extragalactic sources. Fo…
We find that noncritical gravity, a special class of higher derivative gravity, is classically equivalent to Einstein gravity at the full nonlinear level. We obtain the viscosity-to-entropy ratio and the second order transport coefficients of the dual fluid of noncritical gravity to all orders in the coupling of higher derivative terms. We also compute the holographic entanglement entropy in the dual CFT of noncritical gravity. All these results confirm the nonlinear equivalence between noncritical gravity and Einstein gravity at the classical level.
Analogue gravity can be used to reproduce the phenomenology of quantum field theory in curved spacetime and in particular phenomena such as cosmological particle creation and Hawking radiation. In black hole physics, taking into account the backreaction of such effects on the metric requires an extension to semiclassical gravity and leads to an apparent inconsistency in the theory: the black hole evaporation induces a breakdown of the unitary quantum evolution leading to the so called information loss problem. Here we show that analogue gravity can provide an interesting perspective on the res…
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, {\it 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 correctio…
In this paper we perform a full gauge-fixing of the phase space of four dimensional General Relativity (GR) of Lorentzian signature for the time symmetric case, using the CDJ variables. In particular, the Gauss' law constraint in the chosen gauge meets the conditions of the Cauchy-Kovalevskaya theorem for first order, quasilinear PDEs. This implies the existence of a unique analytic solution to the initial value constraints problem in some region of 3-space, featuring four free functions per spacetime point. This result constitutes a step toward addressal of the reduced phase space problem of …
We examine the reduced phase space of the Barbero-Varadarajan solutions of the Ashtekar formulation of (2+1)-dimensional general relativity on a torus. We show that it is a finite-dimensional space due to existence of an infinite dimensional residual gauge invariance which reduces the infinite-dimensional space of solutions to a finite-dimensional space of gauge-inequivalent solutions. This is in agreement with general arguments which imply that the number of physical degrees of freedom for (2+1)-dimensional Ashtekar gravity on a torus is finite.
Building on a recent proposal for a quantum reduction to spherical symmetry from full loop quantum gravity, we investigate the relation between a quantisation of spherically symmetric general relativity and a reduction at the quantum level. To this end, we generalise the previously proposed quantum reduction by dropping the gauge fixing condition on the radial diffeomorphisms, thus allowing to make direct contact between previous work on reduced quantisation. A dictionary between spherically symmetric variables and observables with respect to the reduction constraints in the full theory is dis…
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.
We study the asymptotic behavior of the spherically symmetric solutions of the system obtained from the dimensional reduction of the six-dimensional Einstein- Gauss-Bonnet action. We show that in general the scalar field that parametrizes the size of the internal space is not trivial, but nevertheless the solutions depend on a single parameter. In analogy with other models containing Gauss-Bonnet terms, naked singularities are avoided if a minimal radius for the horizon is assumed.
A Dirac spinor is coupled to topologically massive gravity and the D=3 dimensional action is reduced to D=2 dimensions with a metric that includes both the electromagnetic potential 1-form A and a dilaton scalar ϕ. The dimensionnaly reduced spinor is made a mass eigenstate with a (local) chiral rotation. The non-trivial interactions thus induced are discussed.
Single-vertex Feynman diagrams represent the dominant contribution to physical processes, but are frequently forbidden kinematically. This is changed when the particles involved propagate in a gravitational background and acquire an effective mass. Procedures are introduced that allow the calculation of lowest order diagrams, their corresponding transition probabilities, emission powers and spectra to all orders in the metric deviation, for particles of any spin propagating in gravitational fields described by any metric. Physical properties of the "space-time medium" are also discussed. It is…
Motivated by the analogy proposed by Witten between Chern-Simons and Conformal Field Theories, we explore an alternative way of computing the entropy of a black hole starting from the isolated horizon framework in Loop Quantum Gravity. The consistency of the result opens a window for the interplay between Conformal Field Theory and the description of black holes in Loop Quantum Gravity.
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 qua…
The preceding talks given at this conference have dealt mainly with general ideas for, main problems of and techniques for the task of quantizing gravity canonically. Since one of the major motivations to arrange for this meeting was that it should serve as a beginner's introduction to canonical quantum gravity, we regard it as important to demonstrate the usefulness of the formalism by means of applying it to simplified models of quantum gravity, here formulated in terms of Ashtekar's new variables. From the various, completely solvable, models that have been discussed in the literature we ch…
The evolution of a generally covariant theory is under-determined. One hundred years ago such dynamics had never before been considered; its ramifications were perplexing, its future important role for all the fundamental interactions under the name gauge principle could not be foreseen. We recount some history regarding Einstein, Hilbert, Klein and Noether and the novel features of gravitational energy that led to Noether's two theorems. Under-determined evolution is best revealed in the Hamiltonian formulation. We developed a covariant Hamiltonian formulation. The Hamiltonian boundary term g…
By using a novel technique that establishes a correspondence between general relativity and metric-affine theories based on the Ricci tensor, we are able to set stringent constraints on the free parameter of Born-Infeld gravity from the ones recently obtained for Born-Infeld electrodynamics by using light-by-light scattering data from ATLAS. We also discuss how these gravity theories plus matter fit within an effective field theory framework.
This paper can be seen as an exercise in how to adapt quantum mechanics from a strict relativistic perspective while being respectful and critical towards the experimental achievements of the contemporary theory. The result is a fully observer independent relativistic quantum mechanics for N particle systems without tachyonic solutions. A remaining worry for the moment is Bell's theorem.
Recent developments from the activity of the CGM Group are discussed. Cosmological implications of fundamental approaches to quantization of gravity are presented in order to fix the main issues as well as perspectives for future investigations. Particular attention will be devoted to the classical and quantum features of the generic inhomogeneous Universe, to the role of reference frame in quantum gravity, and eventually to phenomenological features related with the Kaluza-Klein framework.
In the loop quantum gravity context, there have been numerous proposals to quantize the reduced phase space of a black hole, and develop a classical effective description for its interior which eventually resolves the singularity. However, little progress has been made towards understanding the relation between such quantum/effective minisuperspace models and what would be the spherically symmetric sector of loop quantum gravity. In particular, it is not clear whether one can extract the phenomenological predictions obtained in minisuperspace models, such as the singularity resolution and the …
I consider the possibility that space experiments be used to search for quantum properties of spacetime. On the basis of recent quantum-gravity results, I argue that insight on some quantum properties of spacetime can be obtained with experiments planned for the International Space Station, such as AMS and EUSO, and with satellite gamma-ray telescopes, such as GLAST.
We present here the canonical treatment of spherically symmetric (quantum) gravity coupled to spherically symmetric Maxwell theory with or without a cosmological constant. The quantization is based on the reduced phase space which is coordinatized by the mass and the electric charge as well as their canonically conjugate momenta, whose geometrical interpretation is explored. The dimension of the reduced phase space depends on the topology chosen, quite similar to the case of pure (2+1) gravity. We also compare the reduced phase space quantization to the algebraic quantization. Altogether, we o…
We extend here the canonical treatment of spherically symmetric (quantum) gravity to the most simple matter coupling, namely spherically symmetric Maxwell theory with or without a cosmological constant. The quantization is based on the reduced phase space which is coordinatized by the mass and the electric charge as well as their canonically conjugate momenta, whose geometrical interpretation is explored. The dimension of the reduced phase space depends on the topology chosen, quite similar to the case of pure (2+1) gravity. We investigate several conceptual and technical details that might be…
A sketch of the affine quantum gravity program illustrates a different perspective on several difficult issues of principle: metric positivity; quantum anomalies; and nonrenormalizability.
