Search

A new set of twisted geometric variables is introduced to parametrize the holonomy-flux phase space in loop quantum gravity. It is verified that these new geometric variables, after symplectic reduction with respect to the Gauss constraint, form a Poisson algebra which is analogue to that in quantum mechanics. This property ensures that these new geometric variables provide a simple path measure, upon which a new formulation of coherent state path integral based on twisted geometry coherent state is established in loop quantum gravity. Especially, this path integral is analytically computable by expanding the corresponding effective action around the complex evolution trajectories at second order, and the result gives the semi-classical approximation of the quantum propagator between twisted geometry coherent state in LQG.

We present further applications of the formalism introduced by the authors in arXiv:2308.10949, which allows embedding of a broad class of generalized LTB models into effective spherically symmetric spacetimes. We focus on regular black hole models, where a broad class of models can be considered, including for example LQG-inspired models as well as the model with a regular center, e.g. of Bardeen and Hayward. For a certain class of regular black hole models, we can formulate a Birkhoff-like theorem in LTB coordinates. We further show that depending on the properties of the polymerization functions characterizing such regular black hole models in this formalism, the uniqueness of the effective spherically symmetric vacuum solutions might not be given in general in Schwarzschild-like coordinates. Furthermore, we introduce a reconstruction algorithm that allows for a subclass of this models to construct from a given metric in Schwarzschild-like coordinates the corresponding effective spherically symmetric model, its dynamics as an 1+1-dimensional field theory as well as a corresponding covariant Lagrangian of extended mimetic gravity in four dimensions. Such a reconstruction allows us to obtain Lagrangians of extended mimetic gravity models for black holes with a regular center, e.g. the Bardeen and Hayward metric as well as for effective LQG inspired models. Moreover, the reconstruction enables us to extend regular black hole models to general inhomogeneous dust collapse models. For the latter, within this formalism, we can investigate and look at the physical properties of the models such as the existence of weak shell-crossing singularities from a novel perspective., Comment: 42 pages, 7 figures

This work develops a comprehensive algorithm and a Mathematica program to construct boundary data and compute real and complex critical points in spinfoam amplitudes. Our approach covers both spacelike tetrahedra and triangles in the EPRL model and timelike tetrahedra and triangles in the Conrady-Hnybida extension, aiming at addressing a wide range of physical scenarios such as cosmology and black holes. Starting with a single 4-simplex, we explain how to numerically construct boundary data and corresponding real critical points from any nondegenerate 4-simplex geometry. Extending this to the simplicial complex, we demonstrate the algorithm for constructing boundary data and critical points using examples with two 4-simplices sharing an internal tetrahedron. By revisiting the $\Delta_3$ triangulation with curved geometry, we demonstrate the numerical computation of the real critical point corresponding to the flat geometry and the deformation to the complex critical points. Additionally, the program evaluates the spinfoam action at the critical points and compare to the Regge action., Comment: 34 pages, 36 figures

We study homogenous and isotropic quantum cosmology using the spinfoam formalism of Loop Quantum Gravity (LQG). We define a coupling of a scalar field to the 4-dimensional Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam model. We employ the numerical method of complex critical points to investigate the model on two different simplicial complexes: the triangulations of a single hypercube and two connected hypercubes. We find nontrivial implications for the effective cosmological dynamics. In the single-hypercube model, the numerical results suggest an effective Friedmann equation with a scalar density that contains higher-order derivatives and a scalar potential. The scalar potential plays a role similar to a positive cosmological constant and drives an accelerated expansion of the universe. The double-hypercubes model resembles a symmetric cosmic bounce, and a similar effective Friedmann equation emerges with higher-order derivative terms in the effective scalar density, whereas the scalar potential becomes negligible., Comment: 14 pages, 13 figures

In this article we propose a new construction of the spatial scalar curvature operator in (1+3)-dimensional LQG based on the twisted geometry. The starting point of the construction is to express the holonomy of the spin connection on a graph in terms of the twisted geometry variables, and we check that this expression reproduces the spin connection in terms of triads in a certain continuum limit. The spatial scalar curvature in terms of twisted geometry is obtained by considering the composition of the holonomy of the spin connection on the loops. With the twisted geometry parametrization of the holonomy-flux phase space, we further express the holonomy of the spin connection and the spatial scalar curvature on a graph in terms of fluxes. Finally, they are promoted as well-defined operators by replacing the fluxes with ordered flux operators.

Based on modifications inspired from loop quantum gravity (LQG), spherically symmetric models have recently been explored to understand the resolution of classical singularities and the fate of the spacetime beyond. While such phenomenological studies have provided useful insights, questions remain on whether such models exhibit some of the desired properties such as consistent LTB conditions, covariance and compatibility with the improved dynamics of loop quantum cosmology in the cosmological and LTB sectors. We provide a systematic procedure to construct effective spherically symmetric models encoding LQG modifications as a $1+1$ field theory models encoding these properties following the analysis in our companion paper. As concrete examples of our generalized strategy we obtain and compare with different phenomenological models which have been investigated recently and demonstrate resolution of singularity by quantum geometry effects via a bounce. These include models with areal gauge fixing, a polymerized vacuum solution, polymerized junction conditions and an Oppenheimer-Snyder dust collapse model. An important insight from our approach is that the dynamical equations care about the $\det(e)$ part rather than the square root of the determinant of the spatial metric. As a result, shock solutions which have been argued to exist in some models are found to be absent even if one considers coordinate transformations., Comment: 25 pages,1 figure

We generalize the existing works on the way (generalized) LTB models can be embedded into polymerized spherically symmetric models in several aspects. We re-examine such an embedding at the classical level and show that a suitable LTB condition can only be treated as a gauge fixing in the non-marginally bound case, while in the marginally bound case it must be considered as an additional first class constraint. A novel aspect of our formalism, based on the effective equations of motion, is to derive compatible dynamics LTB conditions for polymerized models by using holonomy and inverse triad corrections simultaneously, whereas in earlier work these were only considered separately. Further, our formalism allows to derive compatible LTB conditions for a vast of class of polymerized models available in the current literature. Within this broader class of polymerizations there are effective models contained for which the classical LTB condition is a compatible one. Our results show that there exist a class of effective models for which the dynamics decouples completely along the radial direction. It turns out that this subsector is strongly linked to the property that in the temporally gauge fixed model, the algebra of the geometric contribution to the Hamiltonian constraint and the spatial diffeomorphism constraint is closed. We finally apply the formalism to existing models from the literature and compare our results to the existing ones., Comment: 31 pages,1 figure

We consider an extended phase space formulation for cosmological and spherically symmetric models in which the choice of a given $\overline{\mu}$-scheme can be implemented dynamically. These models are constructed in the context of the relational formalism by using a canonical transformation on the extended phase space which provides a Kucha\v{r} decomposition of the extended phase space. The resulting model can be understood as a gauge-unfixed model of a given $\overline{\mu}$-scheme. We use this formalism to investigate the restrictions to the allowed $\overline{\mu}$-scheme from this perspective and discuss the differences in the cosmological and spherically symmetric case. This method can be useful, for example, to obtain a $\overline{\mu}$-scheme in a top-down derivation from full LQG to symmetry reduced effective models, where for some models only the $\mu_0$-scheme has been obtained so far., Comment: 16 pages + appendix, accepted by universe, contribution to the special issue "Loop Quantum Gravity: A Themed Issue in Honor of Prof. Abhay Ashtekar"

The complex critical points are analyzed in the 4-dimensional Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam model in the large-$j$ regime. For the 4-simplex amplitude, taking into account the complex critical point generalizes the large-$j$ asymptotics to the situation with non-Regge boundary data and relates to the twisted geometry. For generic simplicial complexes, we present a general procedure to derive the effective theory of Regge geometries from the spinfoam amplitude in the large-$j$ regime by using the complex critical points. The effective theory is analyzed in detail for the spinfoam amplitude on the double-$\Delta_3$ simplicial complex. We numerically compute the effective action and the solution of the effective equation of motion on the double-$\Delta_3$ complex. The effective theory reproduces the classical Regge gravity when the Barbero-Immirzi parameter $\gamma$ is small., Comment: 29 pages, 15 figures

Numerical methods are a powerful tool for doing calculations in spinfoam theory. We review the major frameworks available, their definition, and various applications. We start from $\texttt{sl2cfoam-next}$, the state-of-the-art library to efficiently compute EPRL spin foam amplitudes based on the booster decomposition. We also review two alternative approaches based on the integration representation of the spinfoam amplitude: Firstly, the numerical computations of the complex critical points discover the curved geometries from the spinfoam amplitude and provides important evidence of resolving the flatness problem in the spinfoam theory. Lastly, we review the numerical estimation of observable expectation values based on the Lefschetz thimble and Markov-Chain Monte Carlo method, with the EPRL spinfoam propagator as an example., Comment: 33 pages, 11 figures. Invited chapter for the book "Handbook of Quantum Gravity" (Eds. C. Bambi, L. Modesto and I.L. Shapiro, Springer Singapore, expected in 2023)

We propose a new $\bar{\mu}$-scheme Hamiltonian effective dynamics in the spherical symmetric sector of Loop Quantum Gravity (LQG). The effective dynamics is generally covariant as derived from a covariant Lagrangian. The Lagrangian belongs to the class of extended mimetic gravity Lagrangians in 4 dimensions. We apply the effective dynamics to both cosmology and black hole. The effective dynamics reproduces the non-singular Loop-Quantum-Cosmology (LQC) effective dynamics. From the effective dynamics, we obtain the non-singular black hole solution, which has a killing symmetry in addition to the spherical symmetry and reduces to the Schwarzschild geometry asymptotically near the infinity. The black hole spacetime resolves the classical singularity and approaches asymptotically the Nariai geometry $\mathrm{dS}_2\times S^2$ at the future infinity in the interior of the black hole. The resulting black hole spacetime has the complete future null infinity $\mathscr{I}^+$. Thanks to the general covariance, the effective dynamics can be reformulated in the light-cone gauge. We generalize the covariant $\bar{\mu}$-scheme effective dynamics to the Callan-Giddings-Harvey-Strominger (CGHS) model and apply the light-cone formulation to the CGHS black hole solution with the null-shell collapse. We focus on the effective dynamics projected along the null shell. The result shows that both the 2d scalar curvature and the derivative of dilaton field are finite, in contrast to the divergence in the CGHS model., Comment: 49 pages, 23 figures

Based on the effective dynamics in the $\bar \mu$ scheme of the spherical symmetry reduced model in the reduced phase space formulation of loop quantum gravity (LQG), we investigate the gravitational collapse of a homogeneous dust cloud, with Gaussian dust serving as both the reference field and the source of the gravitational collapse. The effective dynamics from the considered model for a homogeneous dust cloud reduces precisely to the effective dynamics of loop quantum cosmology (LQC) with extrinsic curvature based K-quantization, indicating that the LQC effective dynamics lives as a subsector of the model presented here. In both the marginally bound and the bound cases of the collapse in effective dynamics, the singularity is resolved and replaced by a bounce. Though quantum geometric modification from spatial curvature is not directly included in the K-quantization it does affect the qualitative dynamics of the collapsing dust cloud in the sense that on the one hand for the marginally bound case, the dust cloud bounces once at fixed maximum energy density and on the other hand for the bound case, the dust cloud undergoes infinite cycles of contraction and expansion at energy densities dependent on the dust mass. Finally, the mass threshold for the formation of a trapped surface in each case is found and the matching conditions between the interior collapsing spacetime and an effective exterior static solution are discussed., Comment: 25 pages, 7 figures

The fermion propagator is derived in detail from the model of fermion coupled to loop quantum gravity. As an ingredient of the propagator, the vacuum state is defined as the ground state of some effective fermion Hamiltonian under the background geometry given by a coherent state resembling the classical Minkowski spacetime. Moreover, as a critical feature of loop quantum gravity, the superposition over graphs is employed to define the vacuum state. It turns out that the graph superposition leads to the propagator being the average of the propagators of the lattice field theory over various graphs so that all fermion doubler modes are suppressed in the propagator. This resolves the doubling problem in loop quantum gravity. Our result suggests that the superposition nature of quantum geometry should, on the one hand, resolve the tension between fermion and the fundamental discreteness and, on the other hand, relate to the continuum limit of quantum gravity., Comment: 25+9 pages, 2 figures

The unification of general relativity and quantum theory is one of the fascinating problems of modern physics. One leading solution is Loop Quantum Gravity (LQG). Simulating LQG may be important for providing predictions which can then be tested experimentally. However, such complex quantum simulations cannot run efficiently on classical computers, and quantum computers or simulators are needed. Here, we experimentally demonstrate quantum simulations of spinfoam amplitudes of LQG on an integrated photonics quantum processor. We simulate a basic transition of LQG and show that the derived spinfoam vertex amplitude falls within 4% error with respect to the theoretical prediction, despite experimental imperfections. We also discuss how to generalize the simulation for more complex transitions, in realistic experimental conditions, which will eventually lead to a quantum advantage demonstration as well as expand the toolbox to investigate LQG., Comment: 5 pages, 4 figures. comments are welcome

The fermion doubling problem has an important impact on quantum gravity, by revealing the tension between fermion and the fundamental discreteness of quantum spacetime. In this work, we discover that in Loop Quantum Gravity, the quantum geometry involving superposition of states associated with lattice refinements provides a resolution to the fermion doubling problem. We construct and analyze the fermion propagator on the quantum geometry, and we show that all fermion doubler modes are suppressed in the propagator. Our result suggests that the superposition nature of quantum geometry should resolve the tension between fermion and the fundamental discreteness, and relate to the continuum limit of quantum gravity., Comment: 5 pages, 2 figures, Appendix: 3 pages, 1 figure

This paper focuses on the semiclassical behavior of the spinfoam quantum gravity in 4 dimensions. There has been long-standing confusion, known as the flatness problem, about whether the curved geometry exists in the semiclassical regime of the spinfoam amplitude. The confusion is resolved by the present work. By numerical computations, we explicitly find curved Regge geometries from the large-$j$ Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam amplitudes on triangulations. These curved geometries are with small deficit angles and relate to the complex critical points of the amplitude. The dominant contribution from the curved geometry to the spinfoam amplitude is proportional to $e^{i \mathcal{I}}$, where $\mathcal{I}$ is the Regge action of the geometry plus corrections of higher order in curvature. As a result, the spinfoam amplitude reduces to an integral over Regge geometries weighted by $e^{i \mathcal{I}}$ in the semiclassical regime. As a byproduct, our result also provides a mechanism to relax the cosine problem in the spinfoam model. Our results provide important evidence supporting the semiclassical consistency of the spinfoam quantum gravity., Comment: 5 pages, 12 pages appendix, 4 figures, ILQGS talk: https://tigers.phys.lsu.edu/relativity/ilqgs/qu100521.mp4

This work focuses on Conrady-Hnybida's 4-dimensional extended spinfoam model with timelike polyhedra, while we restrict all faces to be spacelike. Firstly, we prove the absolute convergence of the vertex amplitude with timelike polyhedra, when SU(1,1) boundary states are coherent states or the canonical basis, or their finite linear combinations. Secondly, based on the finite vertex amplitude and a proper prescription of the SU(1,1) intertwiner space, we construct the extended spinfoam amplitude on arbitrary cellular complex, taking into account the sum over SU(1,1) intertwiners of internal timelike polyhedra. We observe that the sum over SU(1,1) intertwiners is infinite for the internal timelike polyhedron that has at least 2 future-pointing and 2 past-pointing face-normals. In order to regularize the possible divergence from summing over SU(1,1) intertwiners, we develop a quantum cut-off scheme based on the eigenvalue of the ``shadow operator''. The spinfoam amplitude with timelike internal polyhedra (and spacelike faces) is finite, when 2 types of cut-offs are imposed: one is imposed on $j$ the eigenvalue of area operator, the other is imposed on the eigenvalue of shadow operator for every internal timelike polyhedron that has at least 2 future-pointing and 2 past-pointing face-normals., Comment: 29 pages

The Lorentzian Engle-Pereira-Rovelli-Livine/Freidel-Krasnov (EPRL/FK) spinfoam model and the Conrady-Hnybida (CH) timelike-surface extension can be expressed in the integral form $\int e^S$. This work studies the analytic continuation of the spinfoam action $S$ to the complexification of the integration domain. Our work extends our knowledge from the real critical points well-studied in the spinfoam large-$j$ asymptotics to general complex critical points of $S$ analytic continued to the complexified domain. The complex critical points satisfying critical equations of the analytic continued $S$. In the large-$j$ regime, the complex critical points give subdominant contributions to the spinfoam amplitude when the real critical points are present. But the contributions from the complex critical points can become dominant when the real critical point are absent. Moreover the contributions from the complex critical points cannot be neglected when the spins $j$ are not large. In this paper, we classify the complex critical points of the spinfoam amplitude, and find a subclass of complex critical points that can be interpreted as 4-dimensional simplicial geometries. In particular, we identify the complex critical points corresponding to the Riemannian simplicial geometries although we start with the Lorentzian spinfoam model. The contribution from these complex critical points of Riemannian geometry to the spinfoam amplitude give $e^{-S_{Regge}}$ in analogy with the Euclidean path integral, where $S_{Regge}$ is the Riemannian Regge action on simplicial complex., Comment: 33 pages; This paper summarizes the results announced at Loops'19 Conference http://gravity.psu.edu/events/loops19/index-loops19.shtml

In the path integral formulation of the reduced phase space Loop Quantum Gravity (LQG), we propose a new approach to allow the spatial cubic lattice (graph) to change dynamically in the physical time evolution. The equations of motion of the path integral derive the effective dynamics of cosmology from the full LQG, when we focus on solutions with homogeneous and isotropic symmetry. The resulting cosmological effective dynamics with the dynamical lattice improves the effective dynamics obtained earlier from the path integral with fixed spatial lattice: The improved effective dynamics recovers the FLRW cosmology at low energy density and resolves the big-bang singularity with a bounce. The critical density $\rho_c$ at the bounce is Planckian $\rho_c\sim \Delta^{-1}$ where $\Delta$ is a Planckian area serving as certain UV cut-off of the effective theory. The effective dynamics gives the unsymmetric bounce and has the de-Sitter (dS) spacetime in the past of the bounce. The cosmological constant $\Lambda_{eff}$ of the dS spacetime is emergent from the quantum effect $\Lambda_{eff}\sim\Delta^{-1}$. These results are qualitatively similar to the properties of $\bar{\mu}$-scheme Loop Quantum Cosmology (LQC). Moreover, we generalize the earlier path integral formulation of the full LQG by taking into account the coupling with an additional real scalar field, which drives the slow-roll inflation of the effective cosmological dynamics. In addition, we discuss the cosmological perturbation theory on the dynamical lattice, and the relation to the Mukhanov-Sasaki equation., Comment: 44 pages, 17 figures

We compute numerically the Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam propagator on a 4-simplex, by adapting the methods of Lefschetz thimble and Markov Chain Monte-Carlo to oscillatory spinfoam integrals. Our method can compute any spinfoam observables at relatively large spins. We obtain the numerical results of the propagators at different spins and demonstrate their consistency with the expected spinfoam semi-classical behavior in the large spin limit. Our results exhibit significant quantum corrections at smaller spins. Our method is reliable and thus can be employed to discover the semi-classical and quantum behaviors of the spinfoam model., Comment: 26 pages, 8 figures, 11 tables

We propose a new model of the spherical symmetric quantum black hole in the reduced phase space formulation. We deparametrize gravity by coupling to the Gaussian dust which provides the material coordinates. The foliation by dust coordinates covers both the interior and exterior of the black hole. After the spherical symmetry reduction, our model is a 1+1 dimensional field theory containing infinitely many degrees of freedom. The effective dynamics of the quantum black hole is generated by an improved physical Hamiltonian ${\bf H}_\Delta$ where the holonomy correction is implemented by the $\bar{\mu}$-scheme regularization with a Planckian area scale $\Delta$. The effective dynamics recovers the semiclassical Schwarzschild geometry at low curvature regime and resolves the black hole singularity with Planckian curvature. Our model predicts that the evolution of the black hole at late time reaches the charged Nariai geometry ${\rm dS}_2\times S^2$ with Planckian radii. The Nariai geometry is stable under linear perturbations but may be unstable by nonperturbative quantum effects. Our model suggests the existence of quantum tunneling of the Nariai geometry and a scenario of black-hole-to-white-hole transition. During the transition, the linear perturbations exhibit chaotic dynamics with Lyapunov exponent $\lambda=2\pi T_{\rm dS}\sim \Delta^{-1/2}$ relating to the Hawking temperature $T_{\rm dS}$ of ${\rm dS}_2$. In addition, the Nariai geometry in our model provides an interesting example of Wheeler's bag of gold and contains infinitely many infrared soft modes with zero energy density. These infrared modes span a Hilbert space carrying a representation of 1-dimensional spatial diffeomorphisms (or the Witt/Virasoro algebra) which are conserved charges of the effective dynamics by ${\bf H}_\Delta$., Comment: 36 pages, 24 figures

A coarse graining technique akin to block spin transformations that groups together fiducial cells in a homogeneous and isotropic universe has been recently developed in the context of loop quantum cosmology. The key technical ingredient was an SU(1, 1) group and Lie algebra structure of the physical observables as well as the use of Perelomov coherent states for SU(1, 1). It was shown that the coarse graining operation is completely captured by changing group representations. Based on this result, it was subsequently shown that one can extract an explicit renormalisation group flow of the loop quantum cosmology Hamiltonian operator in a simple model with dust-clock. In this paper, we continue this line of investigation and derive a coherent state path integral formulation of this quantum theory and extract an explicit expression for the renormalisation-scale dependent classical Hamiltonian entering the path integral for a coarse grained description at that scale. We find corrections to the non-renormalised Hamiltonian that are qualitatively similar to those previously investigated via canonical quantisation. In particular, they are again most sensitive to small quantum numbers, showing that the large quantum number (spin) description captured by so called "effective equations" in loop quantum cosmology does not reproduce the physics of many small quantum numbers (spins). Our results have direct impact on path integral quantisation in loop quantum gravity, showing that the usually taken large spin limit should be expected not to capture (without renormalisation, as mostly done) the physics of many small spins that is usually assumed to be present in physically reasonable quantum states., Comment: 25 pages, 1 figure

We numerically study the next-to-leading order corrections of the Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) 4-simplex amplitude in the large-$j$ expansions. We perform large-$j$ expansions of Lorentzian EPRL 4-simplex amplitudes with two different types of boundary states, the coherent intertwiners and the coherent spin-network, and numerically compute the leading-order and the next-to-leading order $O(1/j)$ contributions of these amplitudes. We also study the dependences of these $O(1/j)$ corrections on the Barbero-Immirzi parameter $\gamma$. We show that they, as functions of $\gamma$, stabilize to finite real constants as $\gamma\to\infty$. Lastly, we obtain the quantum corrections to the Regge action because of the $O(1/j)$ contribution to the spinfoam amplitude., Comment: 24 pages, 5 figures

Using the disformal solution-generating method, we construct new axisymmetric solutions in Degenerate Higher Order Scalar Tensor (DHOST) theories. The method consists in first considering a "seed" known solution in DHOST theories and then performing a disformal transformation of the metric to obtain a new solution. In vacuum, the two solutions are equivalent but they become physically inequivalent when one considers coupling to matter. In that way, we "disform" the stealth Kerr black hole solution and we obtain a first analytic rotating non-stealth solution in DHOST theories, while the associated scalar field is time-dependent with a constant kinetic density. The new solution is characterized by three parameters: the mass, the spin and the disformal parameter which encodes the deviation with respect to the Kerr geometry. We explore some geometrical properties of the novel disformed Kerr geometry which is no more Ricci flat, has the same singularity as the Kerr metric, admits an ergoregion, and is asymptotically flat. Moreover, the hidden symmetry of the Kerr solution is broken, providing an example of a non-circular geometry in a higher order theory of gravity. We also discuss geodesic motions and compute its (disformed) null directions which are interesting tools to understand the causal structure of the geometry. In addition, to illustrate again the potentiality of the disformal solution-generating method, we present another axisymmetric solution for DHOST theories obtained from a disformal transformation of the generalized Kerr solution of Einstein-Scalar gravity., Comment: 21 pages, references added, matched the published version in JCAP

Recently, a new path integral formulation of Loop Quantum Gravity (LQG) has been derived in arXiv:1910.03763 from the reduced phase space formulation of the canonical LQG. This paper focuses on the semiclassical analysis of this path integral formulation. We show that dominant contributions of the path integral come from solutions of semiclassical equations of motion (EOMs), which reduces to Hamilton's equations of holonomies and fluxes ${h}(e),{p}^a(e)$ in the reduced phase space $\mathcal{P}_\gamma$ of the cubic lattice $\gamma$: $\dot{h}(e)=\{{h}(e),\, \mathbf{H}\}$, $\dot{p}^a(e)=\{{p}^a(e),\, \mathbf{H}\}$, where $\mathbf{H}$ is the discrete physical Hamiltonian. The semiclassical dynamics from the path integral becomes an initial value problem of Hamiltonian time evolution in $\mathcal{P}_\gamma$. Moreover when we take the continuum limit of the lattice $\gamma$, these Hamilton's equations reproduce correctly classical reduced phase space EOMs of gravity coupled to dust fields in the continuum, as far as initial and final states are semiclassical. Our result proves that the new path integral formulation has the correct semiclassical limit, and indicates that the reduced phase space quantization in LQG is semiclassically consistent. Based on these results, we compare this path integral formulation and the spin foam formulation, and show that this formulation has several advantages including the finiteness, the relation with canonical LQG, and being free of cosine and flatness problems., Comment: 25+3 pages, no figure. ILQGS talk: http://relativity.phys.lsu.edu/ilqgs/han041420.mp4. Mathematica files can be downloaded from https://github.com/LQG-Florida-Atlantic-University/Classical-EOM

We apply the full theory of Loop Quantum Gravity (LQG) to cosmology and present a top-down derivation of gauge-invariant cosmological perturbation theory from quantum gravity. The derivation employs the reduced phase space formulation of LQG and the new discrete path integral formulation defined in arXiv:1910.03763. We demonstrate that in the semiclassical approximation and continuum limit, the result coincides with the existing formulation of gauge-invariant cosmological perturbation theory in e.g. arXiv:0711.0117. Time evolution of cosmological perturbations is computed numerically from the new cosmological perturbation theory of LQG, and various power spectrums are studied for scalar mode and tensor mode perturbations. Comparing these power spectrums with predictions from the classical theory demonstrate corrections in the ultra-long wavelength regime. These corrections are results from the lattice discretization in LQG. In addition, tensor mode perturbations at late time demonstrate the emergence of spin-2 gravitons as low energy excitations from LQG. The graviton has a modified dispersion relation and reduces to the standard graviton in the long wavelength limit., Comment: 26 pages, 16 figures. ILQGS talk: http://relativity.phys.lsu.edu/ilqgs/han041420.mp4. Mathematica files can be downloaded from https://github.com/LQG-Florida-Atlantic-University/cos_pert

The problem of simulating complex quantum processes on classical computers gave rise to the field of quantum simulations. Quantum simulators solve problems, such as Boson sampling, where classical counterparts fail. In another field of physics, the unification of general relativity and quantum theory is one of the greatest challenges of our time. One leading approach is Loop Quantum Gravity (LQG). Here, we connect these two fields and design a linear-optical simulator such that the evolution of the optical quantum gates simulates the spinfoam amplitudes of LQG. It has been shown that computing transition amplitudes in simple quantum field theories falls into the class BQP -- which strongly suggests that computing transition amplitudes of LQG are classically intractable. Therefore, these amplitudes are efficiently computable with universal quantum computers which are, alas, possibly decades away. We propose here an alternative special-purpose linear-optical quantum computer, which can be implemented using current technologies. This machine is capable of efficiently computing these quantities. This work opens a new way to relate quantum gravity to quantum information and will expand our understanding of the theory., Comment: 5 pages, 3 figures, comments are welcome

In approaches to quantum gravity, where smooth spacetime is an emergent approximation of a discrete Planckian fundamental structure, any effective smooth field theoretical description would miss part of the fundamental degrees of freedom and thus break unitarity. This is applicable also to trivial gravitational field (low energy) idealizations realized by the use of the Minkowski background geometry which, as any other spacetime geometry, corresponds, in the fundamental description, to infinitely many different and closely degenerate discrete microstates. The existence of such microstates provides a large reservoir for information to be coded at the end of black hole evaporation and thus opens the way to a natural resolution of the black hole evaporation information puzzle. In this paper we show that these expectations can be made precise in a simple quantum gravity model for cosmology motivated by loop quantum gravity. Concretely, even when the model is fundamentally unitary, when microscopic degrees of freedom irrelevant to low-energy cosmological observers are suitably ignored, pure states in the effective description evolve into mixed states due to decoherence with the Planckian microscopic structure. Moreover, in the relevant physical regime these hidden degrees freedom do not carry any `energy' and thus realize in a fully quantum gravitational context the idea (emphasized before by Unruh and Wald) that decoherence can take place without dissipation, now in a concrete gravitational model strongly motivated by quantum gravity. All this strengthen the perspective of a quite conservative and natural resolution of the black hole evaporation puzzle where information is not destroyed but simply degraded (made unavailable to low energy observers) into correlations with the microscopic structure of the quantum geometry at the Planck scale.

We propose a new derivation from the full Loop Quantum Gravity (LQG) to the Loop Quantum Cosmology (LQC) improved $\bar{\mu}$-scheme effective dynamics, based on the reduced phase space formulation of LQG and a proposal of effective Hamiltonian/action in the full LQG. A key step of our program is an improved regularization of the full LQG Hamiltonian on a cubic lattice. The improved Hamiltonian uses a set of "dressed holonomies" $h_\Delta(\mathfrak{s})$ which not only depend on the connection $A$ but also depend on the length of the curve $\mathfrak{s}$. With the improved Hamiltonian, we propose a quantum effective action and derive a new set effective equations of motion (EOMs) for the full LQG. Then we show that these new EOMs imply the $\bar{\mu}$-scheme effective dynamics for both the homogeneous-isotropic and Bianchi-I cosmology, and predict bounce and Planckian critical density. As a byproduct, although the model is defined on a cubic lattice, we find that the improved effective Hamiltonian of cosmology is invariant under the lattice refinement. The cosmological effective dynamics, predictions of bounce and critical density are results at the continuum limit., Comment: 16+4 pages, 1 figure