arXiv subjects

Lorenzo Sindoni

Publications and source records attributed to Lorenzo Sindoni.

At least 19 recordsLinked to original sources

arXiv2018

Black Holes as Quantum Gravity Condensates

We model spherically symmetric black holes within the group field theory formalism for quantum gravity via generalised condensate states, involving sums over arbitrarily refined graphs (dual to 3d triangulations). The construction relies heavily on both the combinatorial tools of random tensor models and the quantum geometric data of loop quantum gravity, both part of the group field theory formalism. Armed with the detailed microscopic structure, we compute the entropy associated with the black hole horizon, which turns out to be equivalently the Boltzmann entropy of its microscopic degrees of freedom and the entanglement entropy between the inside and outside regions. We recover the area law under very general conditions, as well as the Bekenstein-Hawking formula. The result is also shown to be generically independent of any specific value of the Immirzi parameter.

gr-qc↗

arXiv2017

Bouncing cosmologies from quantum gravity condensates

We show how the large-scale cosmological dynamics can be obtained from the hydrodynamics of isotropic group field theory condensate states in the Gross-Pitaevskii approximation. The correct Friedmann equations are recovered in the semi-classical limit for some choices of the parameters in the action for the group field theory, and quantum gravity corrections arise in the high-curvature regime causing a bounce which generically resolves the big-bang and big-crunch singularities.

gr-qc↗

arXiv2016

Emergent Friedmann dynamics with a quantum bounce from quantum gravity condensates

We study the effective cosmological dynamics, emerging as the hydrodynamics of simple condensate states, of a group field theory model for quantum gravity coupled to a massless scalar field and reduced to its isotropic sector. The quantum equations of motion for these group field theory condensate states are given in relational terms with respect to the scalar field, from which effective dynamics for spatially flat, homogeneous and isotropic space-times can be extracted. The result is a generalization of the Friedmann equations, including quantum gravity modifications, in a specific regime of the theory corresponding to a Gross-Pitaevskii approximation where interactions are subdominant. The classical Friedmann equations of general relativity are recovered in a suitable semi-classical limit for some range of parameters of the microscopic dynamics. An important result is that the quantum geometries associated with these GFT condensate states are non-singular: a bounce generically occurs in the Planck regime. For some choices of condensate states, these modified Friedmann equations are very similar to those of loop quantum cosmology.

gr-qc↗

arXiv2016

Quantum Cosmology from Group Field Theory Condensates: a Review

We give, in some detail, a critical overview over recent work towards deriving a cosmological phenomenology from the fundamental quantum dynamics of group field theory (GFT), based on the picture of a macroscopic universe as a "condensate" of a large number of quanta of geometry which are given by excitations of the GFT field over a "no-space" vacuum. We emphasise conceptual foundations, relations to other research programmes in GFT and the wider context of loop quantum gravity (LQG), and connections to the quantum physics of real Bose-Einstein condensates. We show how to extract an effective dynamics for GFT condensates from the microscopic GFT physics, and how to compare it with predictions of more conventional quantum cosmology models, in particular loop quantum cosmology (LQC). No detailed familiarity with the GFT formalism is assumed.

gr-qc↗

arXiv2016

On moments of the integrated exponential Brownian motion

We present new exact expressions for a class of moments for the geometric Brownian motion, in terms of determinants, obtained using a recurrence relation and combinatorial arguments for the case of a Ito's Wiener process. We then apply the obtained exact formulas to computing averages of the solution of the logistic stochastic differential equation via a series expansion, and compare the results to the solution obtained via Monte Carlo.

cond-mat.stat-mech↗

arXiv2016

Optimal growth trajectories with finite carrying capacity

We consider the problem of finding optimal strategies that maximize the average growth-rate of multiplicative stochastic processes. For a geometric Brownian motion the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction of resources at any step of the dynamics. We generalize these finding to the case of dynamical equations with finite carrying capacity, which can find applications in biology, mathematical ecology, and finance. We formulate the problem in terms of a stochastic process with multiplicative noise and a non-linear drift term that is determined by the specific functional form of carrying capacity. We solve the stochastic equation for two classes of carrying capacity functions (power laws and logarithmic), and in both cases compute optimal trajectories of the control parameter. We further test the validity of our analytical results using numerical simulations.

q-fin.PM↗

arXiv2016

Horizon entropy from quantum gravity condensates

We construct condensate states encoding the continuum spherically symmetric quantum geometry of an horizon in full quantum gravity, i.e. without any classical symmetry reduction, in the group field theory formalism. Tracing over the bulk degrees of freedom, we show how the resulting reduced density matrix manifestly exhibits an holographic behavior. We derive a complete orthonormal basis of eigenstates for the reduced density matrix of the horizon and use it to compute the horizon entanglement entropy. By imposing consistency with the horizon boundary conditions and semiclassical thermodynamical properties, we recover the Bekenstein--Hawking entropy formula for any value of the Immirzi parameter. Our analysis supports the equivalence between the von Neumann (entanglement) entropy interpretation and the Boltzmann (statistical) one.

gr-qc↗

arXiv2015

Generalized quantum gravity condensates for homogeneous geometries and cosmology

We construct a generalized class of quantum gravity condensate states, that allows the description of continuum homogeneous quantum geometries within the full theory. They are based on similar ideas already applied to extract effective cosmological dynamics from the group field theory formalism, and thus also from loop quantum gravity. However, they represent an improvement over the simplest condensates used in the literature, in that they are defined by an infinite superposition of graph-based states encoding in a precise way the topology of the spatial manifold. The construction is based on the definition of refinement operators on spin network states, written in a second quantized language. The construction lends itself easily to be applied also to the case of spherically symmetric quantum geometries.

gr-qc↗

arXiv2014

Effective equations for GFT condensates from fidelity

The derivation of effective equations for group field theories is discussed from a variational point of view, with the action being determined by the fidelity of the trial state with respect to the exact state. It is shown how the maximisation procedure with respect to the parameters of the trial state lead to the expected equations, in the case of simple condensates. Furthermore, we show that the second functional derivative of the fidelity gives a compact way to estimate, within the effective theory itself, the limits of its validity. The generalisation can be extended to include the Nakajima--Zwanzig projection method for general mixed trial states.

gr-qc↗

arXiv2014

Homogeneous cosmologies as group field theory condensates

We give a general procedure, in the group field theory (GFT) formalism for quantum gravity, for constructing states that describe macroscopic, spatially homogeneous universes. These states are close to coherent (condensate) states used in the description of Bose-Einstein condensates. The condition on such states to be (approximate) solutions to the quantum equations of motion of GFT is used to extract an effective dynamics for homogeneous cosmologies directly from the underlying quantum theory. The resulting description in general gives nonlinear and nonlocal equations for the 'condensate wavefunction' which are analogous to the Gross-Pitaevskii equation in Bose-Einstein condensates. We show the general form of the effective equations for current quantum gravity models, as well as some concrete examples. We identify conditions under which the dynamics becomes linear, admitting an interpretation as a quantum-cosmological Wheeler-DeWitt equation, and give its semiclassical (WKB) approximation in the case of a kinetic term that includes a Laplace-Beltrami operator. For isotropic states, this approximation reproduces the classical Friedmann equation in vacuum with positive spatial curvature. We show how the formalism can be consistently extended from Riemannian signature to Lorentzian signature models, and discuss the addition of matter fields, obtaining the correct coupling of a massless scalar in the Friedmann equation from the most natural extension of the GFT action. We also outline the procedure for extending our condensate states to include cosmological perturbations. Our results form the basis of a general programme for extracting effective cosmological dynamics directly from a microscopic non-perturbative theory of quantum gravity.

gr-qc↗

arXiv2013

Cosmology from Group Field Theory Formalism for Quantum Gravity

We identify a class of condensate states in the group field theory (GFT) approach to quantum gravity that can be interpreted as macroscopic homogeneous spatial geometries. We then extract the dynamics of such condensate states directly from the fundamental quantum GFT dynamics, following the procedure used in ordinary quantum fluids. The effective dynamics is a non-linear and non-local extension of quantum cosmology. We also show that any GFT model with a kinetic term of Laplacian type gives rise, in a semi-classical (WKB) approximation and in the isotropic case, to a modified Friedmann equation. This is the first concrete, general procedure for extracting an effective cosmological dynamics directly from a fundamental theory of quantum geometry.

gr-qc↗

arXiv2013

Quenches and lattice simulators for particle creation

In this paper we propose a framework for simulating thermal particle production in condensed matter systems. The procedure we describe can be realized by means of a quantum quench of a parameter in the model. In order to support this claim, we study quadratic fermionic systems in one and two dimensions by means of analytical and numerical techniques. In particular, we are able to show that a class of observables associated to Unruh--de Witt detectors are very relevant for this type of setup and that exhibit approximate thermalization.

gr-qc↗

arXiv2013

New coherent states and modified heat equations

We clarify the relations between certain new coherent states for loop quantum gravity and the analytically continued heat kernel coherent states, highlighting the underlying general construction, the presence of a modified heat equation as well as the way in which the properties of the heat kernels are automatically inherited by these new states.

gr-qc↗

arXiv2012

Horizon thermodynamics and composite metrics

We examine the conditions under which the thermodynamic behaviour of gravity can be explained within an emergent gravity scenario, where the metric is defined as a composite operator. We show that due to the availability of a boundary of a boundary principle for the quantum effective action, Clausius-like relations can always be constructed. Hence, any true explanation of the thermodynamic nature of the metric tensor has to be referred to an equilibration process, associated to the presence of an H-theorem, possibly driven by decoherence induced by the pregeometric degrees of freedom, and their entanglement with the geometric ones.

gr-qc↗

arXiv2012

Multihorizon regular black holes

We discuss a general procedure to generate a class of (everywhere regular) solutions of Einstein equations that can have an (a-priori fixed) arbitrary number of horizons. We then report on work currently in progress i) to find a suitable classification scheme for the maximal extension of these solutions and ii) to interpret the source term in Einstein equations as an effective contribution arising from higher dimensional and/or modified gravity.

gr-qc↗

arXiv2012

The analogue cosmological constant in Bose-Einstein condensates: a lesson for quantum gravity

For almost a century, the cosmological constant has been a mysterious object, in relation to both its origin and its very small value. By using a Bose-Einstein condensate analogue model for gravitational dynamics, we address here the cosmological constant issue from an analogue gravity standpoint. Starting from the fundamental equations describing a system of condensed bosons, we highlight the presence of a vacuum source term for the analogue gravitational field, playing the role of a cosmological constant. In this simple system it is possible to compute from scratch the value of this constant, to compare it with other characteristic energy scales and hence address the problem of its magnitude within this framework, suggesting a different path for the solution of this longstanding puzzle. We find that, even though this constant term is related with quantum vacuum effects, it is not immediately related to the ground state energy of the condensate. On the gravity side this result suggests that the interpretation and computation of the cosmological term as a form of renormalized vacuum energy might be misleading, its origin being related to the mechanism that instead produces spacetime from its pregeometric progenitor, shedding a different light on the subject and at the same time suggesting a potentially relevant role of analogue models in the understanding of quantum gravity.

gr-qc↗

arXiv2012

Emergent Models for Gravity: an Overview of Microscopic Models

We give a critical overview of various attempts to describe gravity as an emergent phenomenon, starting from examples of condensed matter physics, to arrive to more sophisticated pregeometric models. The common line of thought is to view the graviton as a composite particle/collective mode. However, we will describe many different ways in which this idea is realized in practice.

gr-qc↗

arXiv2012

Coherent states in quantum gravity: a construction based on the flux representation of LQG

As part of a wider study of coherent states in (loop) quantum gravity, we introduce a modification to the standard construction, based on the recently introduced (non-commutative) flux representation. The resulting quantum states have some welcomed features, in particular concerning peakedness properties, when compared to other coherent states in the literature.

gr-qc↗