Solving the problem of time in terms of Dirac observables

• Jorge Pullin (LSU)

We argue that combining Rovelli's evolving constants of the motion with Page and Wootters relational approach solves the issues both approaches face and provides a way of addressing the problem of time in terms of Dirac observables. As a bonus it also allows to tackle the problem of time of arrival in quantum mechanics. The framework is compatible with the approach in terms of POVM's of Hoehn et al. introduced recently.

Black Hole Remnants and White Holes

• Carlo Rovelli (Aix-Marseille University)

I summarize my current understanding of what LQG indicates about what happens where classical GR fails in realistic black holes.

A black hole interior model in Loop Quantum Cosmology

• Guillermo A. Mena Marugán (IEM, CSIC)

The study of the quantum geometry of nonrotating black holes has received a lot of attention within the framework of Loop Quantum Cosmology. This interest has been revitalized since the introduction of an effective model by Ashtekar, Olmedo, and Singh. Despite recent advances, there are certain questions about its quantization that remain open. We complete this quantization taking as starting point an extended phase space formalism. Adopting standard prescriptions in Loop Quantum Cosmology and searching for quantum solutions to the Hamiltonian constraint in a sufficiently large set of states, we show how to build a physical Hilbert space with a continuous range of black hole mass. This fact seems in favour of a conventional classical limit (at least for large masses). We also briefly comment on the extension to the exterior geometry, the introduction of a scalar field, and the consideration of perturbations.

Spherical collapse and black hole evaporation

• Madhavan Varadarajan (Raman Research Institute)

Uniqueness of the Fock quantization of a massless scalar field in Kantowski-Sachs spacetime and its Hamiltonian.

• Alvaro Torres-Caballeros (CSIC, Madrid)

We discuss a criterion to guarantee the uniqueness of the Fock quantization of a massless free scalar field in a Kantowski-Sachs background. In general spacetimes, the infinite ambiguity of choosing a set of annihilation and creation operators leads to non-equivalent Fock representations, a fact that is due to the unavailability of a privileged vacuum state in the theory. In the case of a Kantowski-Sachs spacetime, we show that the problem can be overcome by imposing invariance under the spatial symmetries of the background and a quantum dynamics that admit a unitary implementation. We also show that this criterion fixes the freedom for background-dependent scalings involved in the choice of creation and annihilation variables. The remaining freedom for background-dependent changes can be employed to attain a Hamiltonian for the scalar field that is asymptotically diagonal in the ultraviolet sector. These results may find applications in the quantization of matter fields and perturbations on anisotropic cosmologies and, morevoer, on the interior of nonrotating black hole spacetimes.

Axial Scalar Perturbations in Kantowski-Sachs Spacetimes

• Andrés Mínguez-Sánchez (Instituto de Estructura de la Materia - CSIC)

Recently, there has been a growing interest in investigating homogeneous but anisotropic spacetimes due to their relation with non-rotating, uncharged black hole interiors. We present a description of axial perturbations for a massless scalar field minimally coupled to this geometry. We truncate the action at the quadratic perturbative order and tailor our analysis to compact spatial sections. Perturbations are described in terms of perturbative gauge invariants, linear perturbative constraints, and their canonically conjugate variables. The entire set, encompassing perturbations and homogeneous degrees of freedom, is completed into a canonical one. We employ a hybrid quantization framework, composing a quantum representation of the homogeneous sector using Loop Quantum Cosmology techniques with a conventional field quantization of the perturbations.

An effective metric from group field theory: implications for cosmology

• Lisa Mickel (University of Sheffield)

Group field theory (GFT) is a background independent approach to quantum gravity that has been successfully applied to the cosmological setting and shown to have the potential for rich phenomenology. In this talk we will explore a novel proposal to construct operators in GFT based on symmetries of the action, whose expectation values can be interpreted as giving rise to an effective metric originating directly from the quantum theory. This construction relies on a relational coordinate system spanned by four massless scalar fields. We proceed to investigate the implications of this proposition for a flat homogeneous universe and its perturbations.

Effective LTB and generalized analysis of a dust collapse

• Stefan Weigl (Institute for Quantum Gravity, FAU Erlangen-Nürnberg)

Based on our work of embedding generalized (effective) LTB models into polymerized spherically symmetric models as a 1 + 1 field theory model, I provide in this talk a way to construct effective LTB models that have a dynamically stable LTB condition, obey a notion of covariance and further are consistent with the improved dynamics of LQC. I will show various aspects of this approach and compare it with different phenomenological models by discussing areal gauge fixing, a polymerized vacuum solution and an Oppenheimer-Snyder dust collapse model. It turns out that a symmetric bounce is typical for these models and that shock solutions are absent.

Lessons from DLCQ for physics at null infinity

• Glenn Barnich (Université libre de Bruxelles)

Motivated by issues in the context of asymptotically flat spacetimes at null infinity, we clarify in the simplest example of a massless scalar field in two dimensions several subtleties that arise when setting up the canonical formulation on a single or on two intersecting null hypersurfaces with a special emphasis on the infinite-dimensional global and conformal symmetries, the free data, a consistent treatment of zero modes, matching conditions, implications for quantization of massless versus massive fields.

Subleading structure of asymptotically-flat spacetimes

• Marc Geiller (ENS de Lyon)

TBA

Quantum equivalence principle and de-Sitter space

• Maciej Dunajski (University of Cambridge)

I discuss the impact of the positive cosmological constant on the interplay between the equivalence principle in general relativity, and the rules of quantum mechanics. At the nonrelativistic level, there is an ambiguity in the definition of a phase of a wave function measured by inertial and accelerating observes. This is the cosmological analogue of the Penrose effect, which can also be seen as a nonrelativistic limit of the Unruh effect.

Exploring Quantum Reference Frames - Part I: Frame Dependence and How to Compare Objects across a Superposition

• Viktoria Kabel

When describing a physical system, it is very common to do so with respect to a reference frame - a ruler used to determine the position of a particle, for example, or a clock, which tracks the time that elapses while it is moving. Usually, reference frames are treated as purely classical objects with well-defined properties. But what happens if we take into account the quantum properties of the reference frame itself? This question has motivated a recent wave of research on *quantum reference frames* (QRFs), which investigates how the description of our world changes when described relative to different quantum systems. Changes of QRFs have a variety of interesting implications. Quantum features previously thought to be absolute, such as superposition and entanglement, suddenly become dependent on the frame. In fact, what we even mean by the same location, spin, or even subsystem across different branches of a superposition can change when describing the system with respect to different QRFs. Here, we introduce a generalized, visual framework that provides a deeper understanding of this phenomenon by relating the frame dependence to the fundamental question of how to identify and compare objects across a superposition. This becomes particularly relevant in the context of spacetimes in superposition, where there is a priori no notion of ”the same” or “different” points across the different possible worlds. With this newfound understanding, we explore the implications for scenarios at the interface between quantum physics and gravity, such as the gravitational field sourced by a massive object in superposition.

Exploring Quantum Reference Frames - Part II: Identification of Events, Spacetimes in Superposition, and a Quantum Hole Argument

• Anne-Catherine de la Hamette (University of Vienna / IQOQI Vienna)

Consider a scenario involving a superposition of semiclassical spacetimes. How can one compare points on the different manifolds across the superposition? Due to the diffeomorphism invariance of general relativity, there is a priori no notion of the “same” or “different” points across the branches. In fact, there are multiple ways of relating points or events on the different spacetimes. Here, we make this concrete by using coincidences of four scalar fields to construct a comparison map between all spacetimes in superposition, which allows us to determine whether an event is located at the “same” or “different” points across the branches. Different choices of scalar fields can be understood as different instantiations of quantum reference frames (QRFs), connecting the construction to recent research in the field of quantum foundations. As explicit applications of this formalism, we explore how the localization of events is relative to the choice of QRF and will discuss the implications thereof for indefinite causal order and the locality of interaction. After examining the construction of relational observables, we conclude with a quantum generalization of the famous hole argument. This argument calls into question the metaphysical meaning of not just spacetime points but also the identification between spacetime points across manifolds in superposition.

Carroll and Galilei limits of 3D and 4D ($\Lambda$-)BMS symmetries

• Tomasz Trześniewski (University of Wroclaw)

There are two threads in the research on symmetries of space-time that originated in the 1960s but have been reinvigorated by the increased interest over the past few years: BMS symmetry (later extended by Barnich and Troessaert) and the kinematical symmetries other than Poincare or (anti-)de Sitter (especially the Carroll and Galilei ones). At their intersection, one may consider the Carrollian and Galilean contraction limits of BMS algebras. It turns out that we can consistently define such contractions for 3D BMS and (partially) 3D $\Lambda$-BMS algebras, while in the case of 4D BMS (in the sense of Barnich and Troessaert) we only obtain quasi-Carrollian/Galilean BMS algebras. This can be compared with the recent studies of contractions of the original BMS algebra, in which their authors came to quite different conclusions. Furthermore, in the context of quantum gravity, quantum-group deformations are being generalized to both BMS and various kinematical algebras and hence it should be worthy to also analyze the interplay between the deformations of BMS algebras and their Carrollian or Galilean contractions.

Superposition of Spacetimes in the Laboratory

• Ofek Bengyat (IQOQI Vienna)

I will present [O. Bengyat, A. Di Biagio, M. Christodoulou, M. Aspelmeyer, arXiv:2309.16312, submitted to PRL], where we argue for the equivalence between (i) an experimentally relevant Gravity Induced Entanglement (GIE) experiment and (ii) the original one, which is much less feasible and would require implementation in space. The original one comprises the interaction of two particles prepared in a superposition of two discrete paths [Bose et al, Phys. Rev. Lett. 119, 240401], [Marletto & Vedral Phys. Rev. Lett. 119, 240402]. The feasible one comprises a continuously delocalized (harmonic oscillator) state of motion [Krisnanda et al, npj Quantum Information 6, 12 (2020)]. An important open question has been whether these two different approaches allow to draw the same conclusions on the quantum nature of gravity. To answer this question, we use a path-integral approach to analyse a setup that contains both features: a superposition of two highly delocalized center of mass states. In both cases the appearance of entanglement, within linearised quantum gravity, is due to gravity being in a superposition of distinct geometries. Moreover, we are able to calculate the relativistic corrections to the entanglement. An experimental detection of those would be evidence for participation of both radiative and non-radiative degrees of freedom in GIE. This contributes to the debate around the matter, as the radiative degrees of freedom are considered the only ones relevant in the eyes of some [Anastopoulos et al, arXiv:2103.08044].

Gravity and the Superposition Principle

• Hristu Culetu (Ovidius University)

The relation between gravity and quantum mechanics is investigated in this work. The link is given by the wave packet expansion process, rooted from the Uncertainty Principle. The basic idea is to express the de Broglie wavelength used by Schrodinger for a massive particle in terms of the associated Compton wavelength which is replaced by the Michell-Laplace radius $Gm/c^{2}$ of the spherical object of mass $m ≥ m_{P}$ , where $m_{P}$ is the Planck mass. The wave packet spreading is studying in spherical coordinates, having the width $σ(t)$, expressed in terms of G and c instead of $\hbar$. Therefore,for masses larger than the Planck mass, a faster dispersion rate of $σ(t)$ is obtained, compared to the standard case. The dispersion of the wave packet is observed only by a free falling observer and the process breaks down once the observer hits the surface of the object. Different freely falling observers notice different rates of expansion of the wave packet and the source of gravity is in a quantum superposition. We further confront the Mita formula for the mean energy of the wave packet with the de Broglie-Bohm quantum potential energy when the Schrodinger equation is expressed in the Madelung form.

Diffeomorphism invariant Fock states in LQG

• Waleed Sherif

In this talk, I will present a Fock space structure that can be naturally equipped to the diffeomorphism invariant Hilbert space of loop quantum gravity (LQG), under certain assumptions. In it, the role of one-particle excitations is played by the diffeomorphism invariant states based on graphs with a single (linked) component. While the structure of the single-particle Hilbert space in this context can be arbitrarily complex, I will show that we can, nevertheless, quantitatively write some condensate states of group field theory (GFT) as diffeomorphism invariant coherent Fock states in LQG hence formally bridging between the two approaches. I will also comment on the quantum geometry of these single and multi-particle states and how can they be tentatively interpreted as well as discuss how the coherent states obtained in this work relate to a more general concept of graph coherent states previously proposed by M. Assanioussi (Phys. Rev. D 101, 124022).

From perturbative algebraic QFT to QG

• Kasia Rejzner (University of York)

In this talk, I will demonstrate how methods of (perturbative) algebraic quantum field theory can be applied to certain problems in quantum gravity. I will focus on three aspects: asymptotic safety, diffeomorphism invariant relational observables, fundamental discreteness as a UV regulator for QFT.

Quantum geometry, knots, quivers, and lattice paths

• Piotr Sułkowski (University of Warsaw)

I will discuss how quantum geometry is associated to ensembles of lattice paths, how it captures properties of quiver moduli spaces, and at the same time encodes invariants of knots. Relations between these seemingly unrelated topics arise from dualities in topological string theory and appropriately engineered systems of branes.

Gravitationally induced decoherence models for different matter systems and their applications

• Kristina Giesel (FAU)

In this talk we consider open quantum systems in which either a scalar field or photons are coupled to linearised gravity. We compare the derivation of the corresponding effective dynamics of the matter systems, encoded in a so-called master equation, in a reduced phase space quantisation, and discuss the similarities and differences of the two models. Finally, we discuss possible applications of these models with special emphasis on the comparison with existing phenomenological models.

Gravitationally induced decoherence of single particles

• Max Joseph Fahn (Institute for Quantum Gravity, Erlangen)

By combining the techniques of open quantum systems with GR, it is possible to derive an evolution equation, usually called master equation, that predicts the effective dynamics of a matter system under the influence of gravity, where the latter is treated as environment. In the talk, the master equation derived in arXiv:2206.06397 for gravitationally induced decoherence of a scalar field using Ashtekar variables is applied to the one-particle sector, motivated by the prospect of measuring similar decoherence effects in astroparticles such as neutrinos. Here, we will present the steps required to extract the effective dynamics of a single scalar particle from the field-theoretic master equation: After a projection to the single particle space, the resulting evolution equation is connected to Feynman diagrams through which the underlying field theory of linearised gravity coupled to a scalar field can be interpreted as an effective field theory. Making use of this link, a UV renormalisation is sketched. In a final step, different approximations that cast the master equation into a completely positive one are compared, the resulting decoherence of the single scalar particle is analysed, and possible applications are discussed.

Curvature from internal spacetime geometry

• Charlie Beil (University of Graz)

Internal spacetime geometry was recently introduced with the aim of modeling quantum nonlocality using degenerate spacetime metrics. Such a spacetime is equipped with a set of worldlines for which time is stationary, that is, worldlines with no interior points. Consequently, the dimensions of tangent spaces vary at points where these worldlines intersect, and a projective measurement of spin or polarization corresponds to an actual projection between tangent spaces of different dimensions. Moreover, the standard model particles can be decomposed into particles with such worldlines using the Dirac Lagrangian. In this talk I will give an overview of this geometric framework, and show how spacetime curvature naturally arises.

Should we learn to do physics with global observables?

• Marios Christodoulou (IQOQI Vienna )

I present a synthesis of ideas based on ongoing work with collaborators and inspired from the debate in the context of table top quantum gravity and going all the way back to the hole argument, that suggest invariance under permutations as a fundamental symmetry for quantum gravity. I discuss implications, in particular that all observables would be expected to be global observables.

Why does LIGO have a new 300-meter cavity?

• Jorge Pullin (LSU)

We discuss the role of the new cavity in the LIGO interferometers to address the issue of the quantum noise in the instruments.

Entangled pairs in evaporating black holes

• Beatriz Elizaga Navascues (Louisiana State University)

In this talk we present a QFT study about the entanglement structure of the Hawking effect in evaporating scenarios. For this purpose, first we review the known concept of Hawking partners, as being the field modes that are entangled with, and thus purify, the thermal radiation. Then, we show how the definition of these partners can be generalized to any case where the temperature of the radiation increases over time according to the semiclassical evaporation process. Our explicit computation allows us to study the relative location of radiation and partner modes at past null infinity. Finally, we discuss some physical consequences of our results on the fate of quantum information in gravitational collapse.

Entanglement and Quantum Geometry

• Eugenio Bianchi (Penn State)

We discuss how the entanglement entropy of geometric observables provides a probe of locality and semiclassicality in loop quantum gravity. We use the quantum polyhedron and intertwiner space as a model system that allows us to illustrate concretely this connection.

Asymptotic safety and the road towards running relational observables

• Renata Ferrero

Asymptotic safety is a UV completion of quantum gravity most commonly realized via a non-trivial fixed point of the Functional Renormalization Group (FRG) flow. The FRG takes the metric as the carrier field of the gravitational degrees of freedom, and the effective action functionals depend on the metric in a diffeomorphism-invariant way. In my talk, I will introduce an approach to compute the RG flow of relational observables which evolve from their microscopic expressions towards the full quantum expectation value. As a first application I will consider four scalar fields coupled to gravity to represent the physical coordinate frame from which relational observables can be constructed. This allows access to universal critical exponents of the observables. As such the computation of these scaling relations can serve as a way to compare with different approaches to quantum gravity.

Scalar cosmological perturbations from quantum-gravitational entanglement

• Luca Marchetti (University of New Brunswick)

A major challenge at the interface between quantum gravity and cosmology is to understand how cosmological structures can emerge from physics at the Planck scale. In this talk, I will provide a concrete example of such an emergence process by extracting the physics of scalar and isotropic cosmological perturbations from full quantum gravity, as described by a causally complete Barrett-Crane group field theory model. From the perspective of the underlying quantum gravity theory, cosmological perturbations will be associated with (relational) nearest-neighbor two-body entanglement, providing crucial insights into the potentially purely quantum-gravitational nature of cosmological perturbations. I will also show that at low energies the emergent relational dynamics of these perturbations are perfectly consistent with those of general relativity, while at trans-Planckian scales quantum effects become important. Finally, I will comment on the implications of these quantum effects for the physics of the early universe and outline future research directions.

Effects of the inflaton potential on the primordial power spectrum in Loop Quantum Cosmology

• Jesús Yébana Carrilero (Instituto de Estructura de la Materia IEM-CSIC)

In scenarios of physical interest in Loop Quantum Cosmology, with a preinflationary epoch where the kinetic energy of the inflaton dominates, the analytic study of the dynamics of the primordial fluctuations has already been carried out by neglecting the inflaton potential. In this talk, we develop approximations to investigate the influence of the potential as the period of kinetic dominance gives way to the inflationary regime. Treating the potential as a perturbation, we discuss how it modifies the effective mass that dictates the dynamics of the scalar perturbations, within the framework of hybrid Loop Quantum Cosmology. Compared to previous works, we introduce a transition period that connects the kinetically dominated regime with inflation, as well as the main modifications coming from a slow-roll correction to a purely de Sitter evolution during the inflationary period. Starting from initial conditions given by a non-oscillating vacuum determined by an asymptotic Hamiltonian diagonalization, we then analytically compute the primordial power spectrum for a quadratic inflation potential. We finally explain the corrections that the inflaton potential produces in this spectrum.

Reviving Quantum Geometrodynamics

• Susanne Schander (Perimeter Institute)

Quantum Geometrodynamics represents an early attempt at the canonical quantization of General Relativity. In a seminal paper, DeWitt proposed a formal Hamiltonian constraint operator by substituting canonical momenta with variational derivative operators. However, the rigorous interpretation of this operator has remained elusive due to the highly nonlinear nature of the constraint and the associated issues arising from the multiplication of distributions. Consequently, a well-defined Hilbert space for the theory could not be specified. In this talk, we propose a novel approach to overcome the difficulties faced by Quantum Geometrodynamics. We employ a lattice discretization that adheres as closely as possible to the original formulation, and examine the lattice corrections to the theory. We discuss the steps necessary for obtaining a well-defined continuum limit and explain how to perform calculations in the effective theory. Moreover, we establish Hilbert spaces for the lattice theories that allow for well-defined lattice approximations of all continuum quantities. These Hilbert spaces exhibit a non-standard representation of the canonical commutation relations between the matrix elements of the spatial metric and the conjugate momenta. This approach ensures that states are exclusively supported on positive definite symmetric matrices.

Quantum geometry of the null cone

• Wolfgang Wieland (FAU Erlangen-Nürnberg)

We present a non-perturbative quantization of gravitational null initial data. Our starting point is the characteristic null initial problem for tetradic gravity with a parity-odd Holst term in the bulk. After a basic review about the resulting Carrollian boundary field theory, we introduce a specific class of impulsive radiative data. This class is defined for a specific choice of relational clock. The clock is chosen in such a way that the shear of the null boundary follows the profile of a step function. The angular dependence is arbitrary. Next, we solve the residual constraints, which are the Raychaudhuri equation and a Carrollian transport equation for an SL(2,R) holonomy. We show that the resulting submanifold in phase space is symplectic. Along each null generator, we end up with a simple mechanical system. The quantization of this system is straightforward. Our basic strategy is to start from an auxiliary Hilbert space with constraints. The physical Hilbert space is the kernel of a constraint, which is a combination of ladder operators. The constraint and its hermitian conjugate are second-class. Solving the constraint amounts to imposing a simple recursion relation for physical states. On the resulting physical Hilbert space, the SL(2,R) Casimir is a Dirac observable. This observable determines the spectrum of the two radiative modes. The area at the initial and final cross sections are Dirac observables as well. They have a discrete spectrum, which agrees with earlier results on this topic.

Primordial Black Holes and Loop Quantum Gravity

• Francesca Vidotto

Primordial black holes have grown in popularity as a dark matter candidate. Different mass spectrum for them are currently under consideration. In this talk I discuss how Loop Quantum Cosmology can integrate the presence of primordial black holes, either in an inflationary scenario or in a ekpyrotic scenario. I review some recent results and discuss the current work in progress. I focus in particular on the possibility of primordial black holes being in the form of black holes remnants: I review the process of creating the remnants from a black-to-while hole transition and the phenomenology associated to them as dark matter.

Spin foam amplitude of the black-to-white hole transition

• Cong Zhang

At the end of Hawking evaporation, as the black hole horizon approaches the Planck scale, the effects of quantum gravity become significant. Based on the conjecture that these quantum gravity effects may induce the transition of the black hole into a white hole, this transition amplitude is studied within the framework of the spin foam model. The spin foam amplitude is built on a 2-complex containing 56 vertices. The boundary state in the amplitude is selected as the Thiemann's complexifier coherent state resembling the semiclassical geometry. Taking into account the fact that triad fields of different orientations, i.e., $e_i^a$ and $-e_i^a$, give the same intrinsic geometry of the boundary, we creatively adopt the the boundary state as the superposition of the coherent states associated with the both orientations. We employ the method of complex critical point to numerically compute the transition amplitude. Despite the numerical results, it is interestingly found that the transition amplitude is dominated by the terms allowing the change in orientation. This finding suggests that the black-to-white hole transition should be accompanied by the tunneling process of a change in orientation.

Effective theory for regular black holes

• Hongguang Liu (FAU Erlangen)

Recently, models with different properties have been proposed for regular black holes. To fully understand their properties and differences, we provide a systematic analysis for the classification and construction of effective polymerized spherically symmetric models as $1+1$d field theory. We apply this formalism and consider models that have the following advantages: The effective dynamics can be derived from a class of extended mimetic gravity Lagrangian in 4 dimensions. The models admit a consistent Lemaitre-Tolman-Bondi (LTB) condition, by which the dynamics is completely decoupled along the radial direction in LTB coordinates, trivializing the junction condition in dust collapse. The class of effective dynamics admits a polymerized Birkhoff-like theorem, which leads to a stationary effective metric in the polymerized vacuum. In this talk I will give an overview of this classification and describe the procedure for the reconstruction of the underlying effective dynamics and (inhomogeneous) dust collapse solutions from stationary solutions or vice versa. Examples include several well-known regular black hole solutions, such as the Bouncing, Bardeen, and Hayward black holes.

Status of Birkhoff's theorem in polymerized semiclassical regime of Loop Quantum Gravity

• Luca Cafaro (University of Warsaw)

The collapse of a spherically symmetric ball of pressureless dust has been intensively studied in Loop Quantum Gravity (LQG). From a quantum theory, it is possible to recover a semiclassical regime through a polymerization procedure. In this setting, general solutions to the polymerized Einstein field equations (PEFE) will be discussed both for the interior and the exterior of the dust cloud. Exterior solutions are particularly interesting since they may lead to a semiclassical version of Birkhoff's theorem. It is seen that if time independence of the vacuum is imposed, there exists a unique class of solutions depending on a constant. Nevertheless, the possibility of more intricate time dependent solutions is not ruled out completely. Ultimately, these results will be compared to a model of spherical collapse obtained independently from the Einstein equations.

Second Order Geometry and the Quantum Foam

• Folkert Kuipers (LMU Munich)

The search for a theory that consistently combines quantum theory with general relativity forces us to consider geometrical frameworks beyond standard (first order) differential geometry. One candidate for such a generalized geometrical framework is second order (stochastic) differential geometry, which incorporates a violation of Leibniz rule, that is characteristic to the Wiener integral, into the geometry. This feature makes the framework an ideal tool in the study of covariant path integrals. In this talk, I will review the basic ingredients of this framework in both a Euclidean and Lorentzian signature. I will pay particular attention to the deformations of spacetime symmetries that arise due to the coupling of spacetime fluctuations to the affine connection, and discuss some connections to non-commutative geometry.

Constraining Quantum Gravity Polymer Parameters through Gravitational Wave Observations

• Yaser Tavakoli

In this presentation, I will first discuss the theoretical characteristics of polymerized gravitational waves (GWs). Subsequently, I will present empirical limitations on the polymer scale concerning polymer GWs within a classical background spacetime. These constraints will be derived from variations in the propagation speed of GWs. By leveraging data from reputable sources such as the inter-detector arrival time delays from the LIGO-Virgo Collaboration's GWTC1, and the arrival time disparities between the GW signal GW170817 and its corresponding gamma-ray burst GRB170817A, we will deduce restrictions on the polymer parameters.