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**Von Neumann stability of modified loop quantum cosmologies**

Sahil Saini, Parampreet Singh

Von Neumann stability analysis of quantum difference equations in loop quantized spacetimes has often proved useful to understand viability of quantizations and whether general relativistic description is recovered at small spacetime curvatures. We use this technique to analyze the infrared behavior of quantum Hamiltonian constraint in recently explored modifications of loop quantum cosmology: mLQC-I and mLQC-II, for the spatially flat FLRW model. We investigate the behavior for μo scheme, where minimum area of loops in quantization procedure does not take physical metric into account, and the μ¯ scheme where quantization procedure uses physical metric. The fate of stability of quantum difference equations is tested for massless scalar field as well as with inclusion of a positive cosmological constant. We show that for mLQC-I and mLQC-II, difference equation fails to be von Neumann stable for the μo scheme if cosmological constant is included signaling problematic behavior at large volumes. Both of the modified loop quantum cosmologies are von Neumann stable for μ¯ scheme. In contrast to standard loop quantum cosmology, properties of roots turn out to be richer and intricate. Our results demonstrate the robustness of μ¯ scheme (or `improved dynamics') in loop quantization of cosmological spacetimes even when non-trivial quantization ambiguities of Hamiltonian are considered, and show that μo scheme is non-viable in this setting.

25 pages

arXiv:1901.08161 [pdf, other]

**An octahedron of complex null rays, and conformal symmetry breaking**

Maciej Dunajski, Miklos Långvik, Simone Speziale

We show how the manifold T∗SU(2,2) arises as a symplectic reduction from eight copies of the twistor space. Some of the constraints in the twistor space correspond to an octahedral configuration of twelve complex light rays in the Minkowski space. We discuss a mechanism to break the conformal symmetry down to the twistorial parametrisation of T∗SL(2,C) used in loop quantum gravity.

Submitted 16 May, 2019; v1 submitted 23 January, 2019; originally announced January 2019.

10 pages

arXiv:1905.07251 [pdf, other]

**Evaporating black-to-white hole**

Pierre Martin-Dussaud, Carlo Rovelli

We construct and discuss the form of the (effective) spacetime geometry inside a black hole undergoing a quantum transition to a white hole, taking into account the back-reaction of the component of the Hawking radiation falling into the hole.

Submitted 17 May, 2019; originally announced May 2019.

arXiv:1905.10382 [gr-qc](or arXiv:1905.10382v1 [gr-qc] for this version)

**The cosmology of minimal varying Lambda theories**

Stephon Alexander, Marina Cortês, Andrew R. Liddle, João Magueijo, Robert Sims, Lee Smolin

*(Submitted on 24 May 2019)*

Inserting a varying Lambda in Einstein's field equations can be made consistent with Bianchi identities by allowing for torsion, without the need for adding scalar field degrees of freedom. In the minimal such theory, in the absence of matter Lambda is totally free and undetermined by the field equations. Inclusion of matter ties Lambda algebraically to it, at least in a set up where homogeneity and isotropy are assumed, i.e.\ when there is no Weyl curvature. We show that Lambda is proportional to the matter density, with a proportionality constant that depends on the equation of state. Unfortunately, the proportionality constant becomes infinite for pure radiation, ruling out the minimal theory {\it prima facie}, in spite of its novel internal consistency. It is possible to generalize the theory still without the addition of kinetic terms (which would bring it close to a more conventional quintessence model). We now find a new algebraically-enforced proportionality between Lambda and the matter density. Lambda and radiation may now coexist in a form consistent with Big Bang nucleosynthesis, though this places strict constraints on the single free parameter of the theory, θ. In the matter epoch Lambda behaves just like a dark matter component. Its density is proportional to the baryonic and/or dark matter, and its presence and gravitational effects would need to be included in accounting for the necessary dark matter in our Universe. This is a companion paper to Ref. [1] where the underlying gravitational theory is developed in detail.

Companion paper submitted simultaneously to gr-qc

arXiv:1812.05403 [pdf, ps, other]

**Classical axisymmetric gravity in real Ashtekar variables**

Rodolfo Gambini, Esteban Mato, Javier Olmedo, Jorge Pullin

*(Submitted on 13 Dec 2018 (v1), last revised 30 May 2019 (this version, v2))*

We formulate axisymmetric general relativity in terms of real Ashtekar--Barbero variables. We study the constraints and equations of motion and show how the Kerr, Schwarzschild and Minkowski solutions arise. We also discuss boundary conditions. This opens the possibility of a midisuperspace quantization using loop quantum gravity techniques for spacetimes with axial symmetry and time dependence.

14 pages

arXiv:1904.08370 [pdf, other]

**Typical entropy of a subsystem: Page curve and its variance**

Eugenio Bianchi, Pietro Dona

In a quantum system in a pure state, a subsystem generally has a non-zero entropy because of entanglement with the rest of the system. Is the average entanglement entropy of pure states also the typical entropy of the subsystem? The exact formula for the average ⟨SA⟩ was conjectured by Page in 1995 and later proved. Here we compute the exact formula for the average entropy and v…

Submitted 1 June, 2019; v1 submitted 17 April, 2019; originally announced April 2019.

5 pages

arXiv:1902.03590 [pdf, other]

**Spectral estimators for finite non-commutative geometries**

John W. Barrett, Paul Druce, Lisa Glaser

*(Submitted on 10 Feb 2019 (v1), last revised 3 Jun 2019 (this version, v3))*

A finite non-commutative geometry consists of a fuzzy space together with a Dirac operator satisfying the axioms of a real spectral triple. This paper addreses the question of how to extract information about these geometries from the spectrum of the Dirac operator. Since the Dirac operator is a finite-dimensional matrix, the usual asymptotics of the eigenvalues makes no sense and is replaced by measurements of the spectrum at a finite energy scale. The spectral dimension of the square of the Dirac operator is improved to provide a new spectral measure of the dimension of a space called the spectral variance. Similarly, the volume of a space can be computed from the spectrum once the dimension is known. Two methods of doing this are investigated: the well-known Dixmier trace and a recent improvement due to Abel Stern. Finally, the distance between two geometries is investigated by comparing the spectral zeta functions using the method of Cornelissen and Kontogeorgis. All of these techniques are tested on the explicit examples of the fuzzy spheres and fuzzy tori, which can be regarded as approximations of the usual Riemannian sphere and flat tori. Then they are applied to characterise some random fuzzy spaces using data generated by a Monte Carlo simulation.

27 pages

arXiv:1906.01628 [pdf, other]

**Spectroscopy of spinons in Coulomb quantum spin liquids**

Siddhardh C. Morampudi, Frank Wilczek, Chris R. Laumann

*(Submitted on 4 Jun 2019)*

We calculate the effect of the emergent photon on threshold production of spinons in U(1) Coulomb spin liquids such as quantum spin ice. The emergent Coulomb interaction modifies the threshold production cross-section dramatically, changing the weak turn-on expected from the density of states to an abrupt onset reflecting the basic coupling parameters. The slow photon typical in existing lattice models and materials suppresses the intensity at finite momentum and allows profuse Cerenkov radiation beyond a critical momentum. These features are broadly consistent with recent numerical and experimental results.

5 pages

arXiv:1906.02211 [pdf, other]

**Primordial fluctuations from quantum gravity**

Francesco Gozzini, Francesca Vidotto

We study fluctuations and correlations between spatial regions, generated by the primordial quantum gravitational phase of the universe. We do so by a numerical evaluation of Lorentzian amplitudes in Loop Quantum Gravity, in a non-semiclassical regime. We find that the expectation value of the quantum state of the geometry emerging from the early quantum phase of the universe is a homogeneous spac…

Submitted 5 June, 2019; originally announced June 2019.

8 pages

arXiv:1906.04792 [pdf, ps, other]

**Quantization of dynamical symplectic reduction**

Martin Bojowald, Artur Tsobanjan

A long-standing problem in quantum gravity and cosmology is the quantization of systems in which evolution is generated by a constraint that must vanish on solutions. Here, an algebraic formulation of this problem is presented, together with new structures and results that prove the existence of specific conditions for well-defined evolution to be possible.

Submitted 11 June, 2019; originally announced June 2019.

37 pages

arXiv:1906.02958 [gr-qc](or arXiv:1906.02958v1 [gr-qc] for this version)

**Black hole quantum atmosphere for freely falling observers**

Ramit Dey, Stefano Liberati, Zahra Mirzaiyan, Daniele Pranzetti

*(Submitted on 7 Jun 2019)*

We analyze Hawking radiation as perceived by a freely-falling observer and try to draw an inference about the region of origin of the Hawking quanta. To do so, first we calculate the energy density from the stress energy tensor, as perceived by a freely-falling observer. Then we compare this with the energy density computed from an effective temperature functional which depends on the state of the observer. The two ways of computing these quantities show a mismatch at the light ring outside the black hole horizon. To better understand this ambiguity, we show that even taking into account the (minor) breakdown of the adiabatic evolution of the temperature functional which has a peak in the same region of the mismatch, is not enough to remove it. We argue that the appearance of this discrepancy can be traced back to the process of particle creation by showing how the Wentzel--Kramers--Brillouin approximation for the field modes breaks down between the light ring at 3M and 4M, with a peak at r=3.3M exactly where the energy density mismatch is maximized. We hence conclude that these facts strongly support a scenario where the Hawking flux does originate from a "quantum atmosphere" located well outside the black hole horizon.

arXiv:1906.07113 [pdf, ps, other]

**Generalized Gibbs Ensembles in Discrete Quantum Gravity**

Goffredo Chirco, Isha Kotecha

Maximum entropy principle and Souriau's symplectic generalization of Gibbs states have provided crucial insights leading to extensions of standard equilibrium statistical mechanics and thermodynamics. In this brief contribution, we show how such extensions are instrumental in the setting of discrete quantum gravity, towards providing a covariant statistical framework for the emergence of continuum…

Submitted 17 June, 2019; originally announced June 2019.

8 pages

arXiv:1906.03872 [pdf, ps, other]

**Dynamics of Einstein-Aether Scalar field Cosmology**

Andronikos Paliathanasis, G. Papagiannopoulos, Spyros Basilakos, John D. Barrow

*(Submitted on 10 Jun 2019)*

We study the cosmological evolution of the field equations in the context of Einstein-Aether cosmology by including a scalar field in a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker spacetime. Our analysis is separated into two separate where a pressureless fluid source is included or absent. In particular, we determine the critical points of the field equations and we study the stability of the specific solutions. The limit of general relativity is fully recovered, while the dynamical system admits de Sitter solutions which can describe the past inflationary era and the future late-time attractor. Results for generic scalar field potentials are presented while some numerical behaviours are given for specific potential forms.

arXiv:1906.07876 [pdf, other]

**Gravitational edge modes: From Kac-Moody charges to Poincaré networks**

Laurent Freidel, Etera R. Livine, Daniele Pranzetti

We revisit the canonical framework for general relativity in its connection-vierbein formulation, recasting the Gauss law, the Bianchi identity and the space diffeomorphism bulk constraints as conservation laws for boundary surface charges, respectively electric, magnetic and momentum charges. Partitioning the space manifold into 3D regions glued together th…

Submitted 18 June, 2019; originally announced June 2019.

43 pages

arXiv:1906.05633 [pdf, ps, other]

**Isospectrality of quasinormal modes for black holes beyond Schwarzschild**

Flora Moulin, Aurélien Barrau

The reason why the equations describing axial and polar perturbations of the Schwarzschild black hole have the same spectrum is far from trivial. In this article, we revisit the original proof and try to make it clearer. Still focusing on uncharged and non-rotating black holes, we extend the results to slightly more general metrics.

Submitted 13 June, 2019; originally announced June 2019.

arXiv:1906.00603 [pdf, other]

**Quasinormal modes of black holes in a toy-model for cumulative quantum gravity**

Aurélien Barrau, Killian Martineau, Jeremy Martinon, Flora Moulin

The idea that quantum gravity effects might leak outside the horizon of a black hole has recently been intensively considered. In this study, we calculate the quasinormal modes as a function of the location and amplitude of a generic metric perturbation distorting to the Schwarzschild spacetime. We conclude on the possible observability of quantum metric corrections by current and future gravitati…

Submitted 18 June, 2019; v1 submitted 3 June, 2019; originally announced June 2019.

arXiv:1812.03550 [pdf, other]

**Spin foam models and the Duflo map**

Marco Finocchiaro, Daniele Oriti

We give a general definition of spin foam models, and then of models of 4d quantum gravity based on constraining BF theory. We highlight the construction and quantization ambiguities entering model building, among which the choice of quantization map applied to the B variables carrying metric information after imposing simplicity constraints, and the different strategies for imposing the latter co…

Submitted 18 June, 2019; v1 submitted 9 December, 2018; originally announced December 2018.

20 pages