arXiv subjects

Jibril Ben Achour

Publications and source records attributed to Jibril Ben Achour.

49 records · Page 3Linked to original sources

arXiv2016

Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order

We present all scalar-tensor Lagrangians that are cubic in second derivatives of a scalar field, and that are degenerate, hence avoiding Ostrogradsky instabilities. Thanks to the existence of constraints, they propagate no more than three degrees of freedom, despite having higher order equations of motion. We also determine the viable combinations of previously identified quadratic degenerate Lagrangians and the newly established cubic ones. Finally, we study whether the new theories are connected to known scalar-tensor theories such as Horndeski and beyond Horndeski, through conformal or disformal transformations.

hep-th↗

arXiv2016

New Hamiltonians for loop quantum cosmology with arbitrary spin representations

In loop quantum cosmology, one has to make a choice of SU(2) irreducible representation in which to compute holonomies and regularize the curvature of the connection. The systematic choice made in the literature is to work in the fundamental representation, and very little is known about the physics associated with higher spin labels. This constitutes an ambiguity whose understanding, we believe, is fundamental for connecting loop quantum cosmology to full theories of quantum gravity like loop quantum gravity, its spin foam formulation, or cosmological group field theory. We take a step in this direction by providing here a new closed formula for the Hamiltonian of flat FLRW models regularized in a representation of arbitrary spin. This expression is furthermore polynomial in the basic variables which correspond to well-defined operators in the quantum theory, takes into account the so-called inverse-volume corrections, and treats in a unified way two different regularization schemes for the curvature. After studying the effective classical dynamics corresponding to single and multiple spin Hamiltonians, we study the behavior of the critical density when the number of representations is increased, and the stability of the difference equations in the quantum theory.

gr-qc↗

arXiv2016

A new look at scalar perturbations in loop quantum cosmology: (un)deformed algebra approach using self dual variables

Scalar cosmological perturbations in loop quantum cosmology (LQC) is revisited in a covariant manner, using self dual Ashtekar variables. For real-valued Ashtekar-Barbero variables, this `deformed algebra' approach has been shown to implement holonomy corrections from loop quantum gravity (LQG) in a consistent manner, albeit deforming the algebra of modified constraints in the process. This deformation has serious conceptual ramifications, not the least of them being an effective `signature-change' in the deep quantum regime. In this paper, we show that working with self dual variables lead to an undeformed algebra of hypersurface deformations, even after including holonomy corrections in the effective constraints. As a necessary consequence, the diffeomorphism constraint picks up non-perturbative quantum corrections thus hinting at a modification of the underlying space-time structure, a novel ingredient compared to the usual treatment of (spatial) diffeomorphisms in LQG. This work extends a similar result obtained in the context of spherically symmetric gravity coupled to a scalar field, suggesting that self dual variables could be better suited than their real counterparts to treat inhomogeneous LQG models.

gr-qc↗

arXiv2016

Spherically symmetric sector of self dual Ashtekar gravity coupled to matter: Anomaly-free algebra of constraints with holonomy corrections

Using self dual Ashtekar variables, we investigate (at the effective level) the spherically symmetry reduced model of loop quantum gravity, both in vacuum and when coupled to a scalar field. Within the real Ashtekar-Barbero formulation, the system scalar field coupled to spherically symmetric gravity is known to possess a non closed (quantum) algebra of constraints once the holonomy corrections are introduced, which forbids the loop quantization of the model. Moreover, the vacuum case, while not anomalous, introduces modifications which are usually interpreted as an effective signature change of the metric in the deep quantum region. We show in this paper that both those complications disappear when working with self dual Ashtekar variables, both in the vacuum case and in the case of gravity minimally coupled to a scalar field. In this framework, the algebra of the holonomy corrected constraints is anomaly free and reproduces the classical hypersurface deformation algebra without any deformations. A possible path towards quantization of this model is briefly discussed.

gr-qc↗

arXiv2016

Analytic continuation of the rotating black hole state counting

In loop quantum gravity, a spherical black hole can be described in terms of a Chern-Simons theory on a punctured 2-sphere. The sphere represents the horizon. The punctures are the edges of spin-networks in the bulk which cross the horizon and carry quanta of area. One can generalize this construction and model a rotating black hole by adding an extra puncture colored with the angular momentum J in the 2-sphere. We compute the entropy of rotating black holes in this model and study its semi-classical limit. After performing an analytic continuation which sends the Barbero-Immirzi parameter to +/- i, we show that the leading order term in the semi-classical expansion of the entropy reproduces the Bekenstein-Hawking law independently of the value of J.

gr-qc↗

arXiv2016

Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations

We consider all degenerate scalar-tensor theories that depend quadratically on second order derivatives of a scalar field, which we have identified in a previous work. These theories, whose degeneracy in general ensures the absence of Ostrogradski instability, include the quartic Horndenski Lagrangian as well as its quartic extension beyond Horndeski, but also other families of Lagrangians. We study how all these theories transform under general conformal-disformal transformations and find that they can be separated into three main classes that are stable under these transformations. This leads to a complete classification modulo conformal-disformal transformations. Finally, we show that these higher order theories include mimetic gravity and some particular khronometric theories. They also contain theories that do not correspond, to our knowledge, to already studied theories, even up to field redefinitions.

gr-qc↗

arXiv2015

Towards self dual Loop Quantum Gravity

In this PhD thesis, we introduced a new strategy to investigate the kinematical and physical predictions of self dual Loop Quantum Gravity (LQG) and by-passed the old problem of implementing quantum mechanically the so called reality conditions inherent to the self dual Ashtekar's phase space. We first review the loop quantization of the spherically isolated horizon and the computation of its micro-canonical entropy. Then we present the so called gas of punctures model for the quantum horizon, discussing its results in the canonical and grand-canonical ensembles and its limits. The fourth chapter is devoted to studying to what extend the loop quantization based on the self dual variables could cure those problems. We introduce a new strategy, based on an analytic continuation of the degeneracy from $γ\in R$ to $γ= \pm i$. We review in details the construction of the procedure, and present the results. At the leading term, we recover exactly the Bekenstein-Hawking area law. The fifth chapter is devoted to understanding more precisely the interplay between the status of the Immirzi parameter. In order to do this, we introduce from a new toy model describing $2+1$ gravity which depends explicitly on the Immirzi parameter. Finally, the sixth chapter is devoted to applying our procedure to the simplest Loop Quantum Cosmology model. By first constructing the LQC dynamics for any arbitrary spin j and then implementing our analytic continuation, we show that our procedure preserves the key features of the LQC models, i.e. we obtain a bouncing universe which admits the right semi classical limit after the bounce.

gr-qc↗

arXiv2015

Analytic continuation of real Loop Quantum Gravity : Lessons from black hole thermodynamics

This contribution is devoted to summarize the recent results obtained in the construction of an "analytic continuation" of Loop Quantum Gravity (LQG). By this, we mean that we construct analytic continuation of physical quantities in LQG from real values of the Barbero-Immirzi parameter $γ$ to the purely imaginary value $γ= \pm i$. This should allow us to define a quantization of gravity with self-dual Ashtekar variables. We first realized in [1] that this procedure, when applied to compute the entropy of a spherical black hole in LQG for $γ=\pm i$, allows to reproduce exactly the Bekenstein-Hawking area law at the semi-classical limit. The rigorous construction of the analytic continuation of spherical black hole entropy has been done in [2]. Here, we start with a review of the main steps of this construction: we recall that our prescription turns out to be unique (under natural assumptions) and leads to the right semi-classical limit with its logarithmic quantum corrections. Furthermore, the discrete and $γ$-dependent area spectrum of the black hole horizon becomes continuous and obviously $γ$-independent. Then, we review how this analytic continuation could be interpreted in terms of an analytic continuation from the compact gauge group $SU(2)$ to the non-compact gauge group $SU(1,1)$ relying on an analysis of three dimensional quantum gravity.

gr-qc↗

arXiv2014

Black holes as gases of punctures with a chemical potential: Bose-Einstein condensation and logarithmic corrections to the entropy

We study the thermodynamical properties of black holes when described as gases of indistinguishable punctures with a chemical potential. In this picture, which arises from loop quantum gravity, the black hole microstates are defined by finite families of half-integers spins coloring the punctures, and the near-horizon energy measured by quasi-local stationary observers defines the various thermodynamical ensembles. The punctures carry excitations of quantum geometry in the form of quanta of area, and the total horizon area $a_\text{H}$ is given by the sum of these microscopic contributions. We assume here that the system satisfies the Bose-Einstein statistics, and that each microstate is degenerate with a holographic degeneracy given by $\exp\big(λa_\text{H}/\ell_\text{Pl}^2\big)$ and $λ>0$. We analyze in detail the thermodynamical properties resulting from these inputs, and in particular compute the grand canonical entropy. We explain why the requirements that the temperature be fixed to the Unruh temperature and that the chemical potential vanishes do not specify completely the semi-classical regime of large horizon area, and classify in turn what the various regimes can be. When the degeneracy saturates the holographic bound ($λ=1/4$), there exists a semi-classical regime in which the subleading corrections to the entropy are logarithmic. Furthermore, this regime corresponds to a Bose-Einstein condensation, in the sense that it is dominated by punctures carrying the minimal (or ground state) spin value $1/2$.

gr-qc↗

arXiv2014

Loop Quantum Cosmology with Complex Ashtekar Variables

We construct and study Loop Quantum Cosmology (LQC) when the Barbero-Immirzi parameter takes the complex value $γ=\pm i$. We refer to this new quantum cosmology as complex Loop Quantum Cosmology. We proceed in making an analytic continuation of the Hamiltonian constraint (with no inverse volume corrections) from real $γ$ to $γ=\pm i$ in the simple case of a flat FLRW Universe coupled to a massless scalar field with no cosmological constant. For that purpose, we first compute the non-local curvature operator (defined by the trace of the holonomy of the connection around a fundamental plaquette) evaluated in any spin $j$ representation and we find a new close formula for it. This allows to define explicitly a one parameter family of regularizations of the Hamiltonian constraint in LQC, parametrized by the spin $j$. It is immediate to see that any spin $j$ regularization leads to a bounce scenario. Then, motivated particularly by previous results on black hole thermodynamics, we perform the analytic continuation of the Hamiltonian constraint defined by $γ=\pm i$ and $j=-1/2+is$ where $s$ is real. Even if the area spectrum is now continuous, we show that the so-defined complex LQC removes also the original singularity which is replaced by a quantum bounce. In addition, the maximal density and the minimal volume of the Universe are obviously independent of $γ$. Furthermore, the dynamics before and after the bounce are no more symmetric, which makes a clear distinction between these two phases of the evolution of the Universe.

gr-qc↗

arXiv2014

Analytic Continuation of Black Hole Entropy in Loop Quantum Gravity

We define the analytic continuation of the number of black hole microstates in Loop Quantum Gravity to complex values of the Barbero-Immirzi parameter $γ$. This construction deeply relies on the link between black holes and Chern-Simons theory. Technically, the key point consists in writing the number of microstates as an integral in the complex plane of a holomorphic function, and to make use of complex analysis techniques to perform the analytic continuation. Then, we study the thermodynamical properties of the corresponding system (the black hole is viewed as a gas of indistinguishable punctures) in the framework of the grand canonical ensemble where the energy is defined á la Frodden-Gosh-Perez from the point of view of an observer located close to the horizon. The semi-classical limit occurs at the Unruh temperature $T_U$ associated to this local observer. When $γ=\pm i$, the entropy reproduces at the semi-classical limit the area law with quantum corrections. Furthermore, the quantum corrections are logarithmic provided that the chemical potential is fixed to the simple value $μ=2T_U$.

gr-qc↗

arXiv2013

Spectra of geometric operators in three-dimensional LQG: From discrete to continuous

We study and compare the spectra of geometric operators (length and area) in the quantum kinematics of two formulations of three-dimensional Lorentzian loop quantum gravity. In the SU(2) Ashtekar-Barbero framework, the spectra are discrete and depend on the Barbero-Immirzi parameter $γ$ exactly like in the four-dimensional case. However, we show that when working with the self-dual variables and imposing the reality conditions the spectra become continuous and $γ$-independent.

gr-qc↗

arXiv2013

Testing the role of the Barbero-Immirzi parameter and the choice of connection in Loop Quantum Gravity

We study the role of the Barbero-Immirzi parameter $γ$ and the choice of connection in the construction of (a symmetry-reduced version of) loop quantum gravity. We start with the four-dimensional Lorentzian Holst action that we reduce to three dimensions in a way that preserves the presence of $γ$. In the time gauge, the phase space of the resulting three-dimensional theory mimics exactly that of the four-dimensional one. Its quantization can be performed, and on the kinematical Hilbert space spanned by SU(2) spin network states the spectra of geometric operators are discrete and $γ$-dependent. However, because of the three-dimensional nature of the theory, its SU(2) Ashtekar-Barbero Hamiltonian constraint can be traded for the flatness constraint of an sl(2,C) connection, and we show that this latter has to satisfy a linear simplicity-like condition analogous to the one used in the construction of spin foam models. The physically relevant solution to this constraint singles out the non-compact subgroup SU(1,1), which in turn leads to the disappearance of the Barbero-Immirzi parameter and to a continuous length spectrum, in agreement with what is expected from Lorentzian three-dimensional gravity.

gr-qc↗