Quantum cosmology:

Chris Beetle, Florida Atlantic University: A diffeomorphism-invariant cosmological sector of loop quantum gravity

This talk will summarize a scheme to define a sector of homogeneous and isotropic states of loop quantum gravity at the diffeomorphism-invariant level, and to embed the state space of loop quantum cosmology into that sector. It will focus on developing methods to compare dynamics and observables in the two theories.

Jibril BEN ACHOUR, Fudan University, Shanghai, China: The Thiemann Complexifier in Loop Cosmology

We will present recent work where, in the context of Loop Quantum Cosmology, we study the fate of the complexifier, that is the generator of the canonical transformations shifting the Immirzi parameter, for the flat, homogeneous and isotropic FRW cosmology. We will focus on the closed CVH algebra for canonical general relativity consisting in the complexifier, the 3d volume and the Hamiltonian constraint. In standard cosmology, for gravity coupled to a scalar field, the CVH algebra is identified as a su(1,1) Lie algebra, with the Hamiltonian as a null generator and the complexifier as a boost. The su(1,1) Casimir is given by the matter density. In the loop gravity cosmology approach, the gravitational Hamiltonian is regularized in terms of SU(2) holonomies. In order to keep a closed CVH algebra, we show that the complexifier and inverse volume factor needs to be similarly regularized. Then the su(1,1) Casimir is given by the matter density and the volume gap. The action of the Hamiltonian constraints and the complexifier can be exactly integrated. This is straightforward to extend to the quantum level: the cosmological evolution is described in terms of SU(1,1) coherent states and the regularized complexifier generates unitary transformations. This means that, in the physical Hilbert space, the Immirzi ambiguity is to be distinguished from the volume gap, it can be rescaled unitarily and ultimately disappears from physical predictions of the theory. Finally, we show that the complexifier becomes the effective Hamiltonian when deparametrizing the dynamics using the scalar field as a clock, thus underlining the deep relation between cosmological evolution and scale transformations. This new realisation of LQC opens up new perspectives both for the full theory and for the quantisation of symmetry reduced systems with local degrees of freedom.

Eugenio Bianchi, Pennsylvania State University: Emergence of space-like correlations in loop quantum gravity

The vacuum state of a quantum field in a curved space-time has non-trivial correlations at space-like separation. The stretching and squeezing of such correlations plays a crucial role in inflationary cosmology. In this talk I discuss a pre-inflationary scenario where space-like correlations of quantum perturbations arise from an initially unentangled state in loop quantum gravity. This scenario relies on recent results on squeezed vacua and entanglement in loop quantum gravity.

Jakub Bilski, Fudan University: Matter fields in the framework of reduced loop gravity

Considering the sector of LQG that describes the models with diagonal spatial component of the metric, I will show how to construct well defined HCO's for all the Standard Model fields and gravity. I will present how at the leading order, the actions of HCO's reproduce the appropriate classical expressions. The next to the leading order corrections can be considered as perturbations in the Effective Hamiltonian Equation (EHE). I will point out the role of a proper weight of observables and an idea how to tame lattice corrections arising from matter degrees of freedom.

Joseph Bunao, Ateneo de Manila University: An Essentially Self-Adjoint Spacetime Four-Volume Operator in Unimodular Loop Quantum Cosmology

This study constructs an essentially self-adjoint operator $hat{T}$ corresponding to the classical on-shell spacetime four-volume $tilde{T}$ in the context of unimodular loop quantum cosmology for a finite patch of homogeneous and isotropic spacetime with flat spatial slices and no matter sources. As shown in [J. Bunao, Class. Quant. Grav. 34, 035003 (2017)], the action of $hat{T}$ on states in the usual kinematic Hilbert space $mathcal{H}^{kin}$ of loop quantum cosmology is derived from its commutation relation with $hat{Lambda}$ - the operator corresponding to the on-shell cosmological “constant” $tilde{Lambda}$ canonically conjugate to $tilde{T}$. An appropriate domain $D(hat{T})$ is assigned to $hat{T}$ in a separable Hilbert subspace $mathcal{H}_0 subset mathcal{H}^{kin}$ so that its eigenstates $Phi^{e backslash o}_m in D(hat{T})$ are orthonormal with corresponding real and discrete eigenvalues $tau^{e backslash o}_m$. It is then shown that the eigenstates $Phi^{e backslash o}_m$ form a complete set and that $hat{T}$ is indeed essentially self-adjoint in $mathcal{H}_0$.

Marco de Cesare, King's College London: Cosmological implications of the group field theory approach to quantum gravity

I will discuss the impact of quantum gravity effects for cosmology, considering the emergent spacetime scenario based on the group field theory framework. Considering some simple models, I will show that there are significant departures from the standard picture for the history of our Universe, both at early and late times. In particular, I will show how it is possible to achieve a bounce and an early epoch of accelerated expansion in this approach. (based on Phys.Lett. B764 (2017) 49-53 and Phys.Rev. D94 (2016) no.6, 064051)

Jonathan Engle, Florida Atlantic University: Uniqueness of the kinematical Hilbert space of LQC with curved edges

The two new key elements in this work are (1.) the inclusion (as in full LQG) of holonomies along non-straight analytic edges in the basic algebra of LQC, building on the work of Fleischhack, and (2.) the proof that invariance under residual diffeomorphisms and existence of a self-adjoint momentum operator are sufficient to uniquely fix the resulting kinematical Hilbert space. Quite remarkably, this Hilbert space is none other than the standard one used in LQC up until now, even though the standard LQC Hilbert space was derived with only holonomies along straight edges. In addition, a derivation of the LQC phase space from scratch via symmetry reduction of the Holst action and its Dirac analysis, is presented for the first time. This work was published in papers with Maximilian Hanusch and Thomas Thiemann.

Sean Gryb, University of Bristol: Singularity resolution with dynamical quantum geometry

We offer a new proposal for singularity resolution in quantum cosmology based upon quantum evolution. In particular, we advocate a new approach to the quantization of mini-superspace leading to a Schrodinger equation for the universe. For models with a massless scalar field and cosmological constant we show that: i) well-behaved quantum observables can be constructed; ii) self-adjoint extensions of the Hamiltonian lead to unitary, non-singular evolution; and iii) specific solutions display novel phenomenology including a cosmic bounce, the necessity of a positive cosmological constant in the semi-classical limit, and an effective inflationary epoch.

Mercedes Martín-Benito, Instituto de Astrofísica e Ciências do Espaço, Universidade de Lisboa: Dirac fields in cosmology: unitary dynamics as a uniqueness quantization criterion

The Fock quantization of fields is in general subject to an infinite ambiguity, even for free field theories. In order to fix the quantization, we ask for a unitary implementation of the classical symmetries. However in non-stationary backgrounds this is generally not sufficient. In such situations, the additional criterion of a unitary implementation of the dynamics might be the key to remove the ambiguity. This is a non-trivial requirement, as Bogoliubov transformations, like those describing the field dynamics, might not be implementable as unitary operators in Fock space. We investigate this issue in the case of a Dirac field propagating on a homogeneous and isotropic cosmological background. Our main result is that the criterion of unitarity of the dynamics indeed selects a unique Fock quantization (up to unitary equivalence). To obtain it, we first characterize the Fock representations for the canonical anticommutation relations that admit a unitary implementation of the field evolution. Then, once a convention for the notion of particles and antiparticles is set, we show that these representations are all unitarily equivalent.

Killian Martineau, Laboratoire Physique Subatomique et Cosmologie: New results on the background dynamics and perturbations in LQC

In this talk, I will present several clarifications recently derived in loop quantum cosmology. Firstly, I will address the issue of the robustness of the LQC predictions for the background dynamics when varying several fundamental unknown parameters: the initial conditions, the amount of shear at the bounce, and the shape of the inflaton potential. Secondly, I will address the trans-plackian issue. As a first phenomenological step in this direction I will show the consequences of implementing modified dispersion relations.

Guillermo A. Mena Marugán, Instituto de Estructura de la Materia, CSIC.: Title: Fermions in hybrid loop quantum cosmology

We introduce Dirac fields in hybrid loop quantum cosmology and discuss their treatment as primordial perturbations, additional to those of the geometry and the inflaton field. Adopting a Born-Oppenheimer ansatz, we show how to deduce a Schrodinger equation that dictates the quantum evolution of these fermionic perturbations. Remarkably, such evolution is unitary, and couples the fermion field with an infinite sequence of quantum moments of the homogeneous geometry. We also investigate issues related with the quantum backreaction produced by the Dirac fields.

Phillip Mendonca, Florida Atlantic University: Embedding FLRW into Bianchi I, and Other (Relatively) Simple Tasks

This talk will discuss the application of the embedding procedure introduced in the talk by C. Beetle to Bianchi I and other toy models, with the intent to exhibit successes to be expected and challenges to be faced when embedding into the full LQG.

Flavio Mercati, University of Rome `La Sapienza': Shape Dynamics: doing physics with 3D conformal geometry

This is an update on the status of Shape Dynamics, a theory which assumes that the reduced configuration space of gravity is conformal superspace. Using York's method, one can build Einstein spacetimes using only curves in conformal superspace. This allows to describe spacetime with 3D conformal geometry, and also to define a dynamics on conformal superspace that is classically equivalent to that of GR. The equivalence, however, fails in certain situations: at the Big Bang and in presence of horizons. The conformal dynamics can be continued uniquely past these points, and leads to a prescription for gluing together regions of spacetime that admit a CMC foliation. This has interesting consequences for cosmology and the theory of black holes, and possibly for the quantum theory.

Javier Olmedo, Pennsylvania State University: Perturbations in anisotropic loop quantum cosmology spacetimes

Here, we analyze the evolution of primordial perturbations in anisotropic spacetimes (Bianchi I). We start by identifying gauge-invariant scalar and tensor perturbations following a canonical formalism. Then, we characterize the classical space of solutions to the equations of motion with scalar-tensor and tensor-tensor couplings. We adopt a Fock representation where these interactions are not treated perturbatively. For a given choice of vacuum state, we compute the 2-point functions of the quantum perturbations. Eventually, we discuss the consequences of the presence of anisotropies in standard general relativity and loop quantum cosmology, and the predictions that could eventually be compared with observations.

Abdulmajid Osumanu, University of Waterloo: Bicrossproduct model in 3d quantum gravity

It is well-known that the Drinfeld quantum double is relevant to 3d quantum gravity, either in the BF formulation or the Chern-Simons formulation. Different recent works by Osei, Majid and Schroers, have shown how semi-dualization can give rise to the bicrossproduct quantum group from the quantum double. This was specifically used in the Chern-Simons formulation and the semi-dualization is associated to passing to different regimes. We intend to discuss such semi-dualization procedure in the BF formulation. Interestingly this could be relevant to quantum information models such as Kitaev?s model. This is work done in collaboration with Prince Osei and Florian Girelli.

Tomasz Pawłowski, Center for Theoretical Physics, Polish Academy of Science: (Loop) quantum dynamics of Bianchi I universe

The dynamics of flat anisotropic homogeneous universe with matter is studied on the genuine quantum level within the strict formulation of impruved dynamics of the loop quantum cosmology framework.

Andreas Pithis, King's College London: Aspects of GFT condensate cosmology

In the context of the Group field theory (GFT) quantum gravity condensate analogue of the Gross-Pitaevskii equation for Bose-Einstein condensates (BEC), we analyze the behaviour of static and relationally evolving GFT models with effective interactions. More precisely, we firstly study the expectation value of the volume operator imported from Loop Quantum Gravity (LQG) in an isotropic restriction for a free and then interacting condensate system. For these one finds a non-vanishing condensate population which is dominated by the lowest nontrivial configurations of the quantum geometry. This suggests that the condensate consists of many smallest building blocks giving rise to an effectively continuous geometry and that the interpretation of the condensate to correspond to a geometric phase might be appropriate. In a second step, we study the relational evolution of initially anisotropic condensate systems, demonstrate that they quickly isotropize and that from their effective dynamics the classical Friedmann equation can be recovered. The talk is (mostly) based on the material presented in the articles arXiv:1607.06662, 1612.02456, 1606.00352.

Giorgio Sarno, Università di Torino: From Analytical to Numerical: The EPLR 4-Simplex Asymptotic Behavior

We present different analytic and numerical results for the Lorentzian EPRL model. These include the details of the factorization procedure and the structure and behavior of the edge propagators, which allows us to establish scaling properties. We then focus on the case of a 4-simplex amplitude, providing the first numerical evidence of Barrett’s asymptotic formula for the EPRL model. We show that for Euclidean boundary data, the asymptotic is directly inherited from the factorized SU(2) 15j symbol. For Lorentzian boundary data we uncover the key role the edge propagators plays in the asymptotic behavior of the 4-simplex EPLR amplitude.

David Sloan, University of Oxford: Through the Big Bang

I will show how the intrinsic definition of observables in relativity through dynamical similarity leads to the continuation of Einstein's equations classically through the big bang singularity in simple cosmological scenarios. By appealing to general principles I argue that this is a generic feature, and that the singularity can be viewed as an artifact of the redundant description imposed by absolute length scales. I will then lay out some other welcome features of intrinsic relational systems, and discuss the broader questions raised by a theory of physics that is independent of physical dimensions such as mass and length.

Gabriele Vittorio Stagno, Dipartimento di Fisica, "Sapienza" Università di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy: Lorentian generalized spinfoams and dipole cosmology

We study generalised KKL-spin foams for the Lorentzian EPRL model with two dipole boundary graphs, and applications to cosmology. We discuss integrability conditions and properties of partial foam resummations based on scaling laws. We present analytical and numerical results that show an unexpected strong factorisation property and complete lack of oscillations that raise delicate questions on the use of non-simplicial spin foams.

Ilya Vilensky, Florida Atlantic University: Spinfoam cosmology with the proper vertex amplitude

The proper vertex amplitude is derived from the EPRL vertex by restricting to a single gravitational sector in order to achieve the correct semi-classical behaviour. We apply the proper vertex to calculate a cosmological transition amplitude that can be viewed as the Hartle-Hawking wavefunction. To perform this calculation we deduce the integral form of the proper vertex and use extended stationary phase methods to estimate the large-volume limit. We show that the resulting amplitude satisfies an operator constraint whose classical analogue is the Hamiltonian constraint of the Friedmann-Robertson-Walker cosmology. We find that the constraint dynamically selects the relevant family of coherent states and demonstrate a similar dynamic selection in standard quantum mechanics. The effects of dynamical selection on long-range correlations are analyzed.

Anzhong Wang, Baylor University: Pre-inflationary universe in loop quantum cosmology

The evolutions of the flat FLRW universe and its linear perturbations are studied systematically in {em the dressed metric approach} of LQC. When the evolution of the background at the quantum bounce is dominated by the kinetic energy of the inflaton, it can be divided into three different phases prior to the preheating, {em bouncing, transition and slow-roll inflation}. During the bouncing phase, the evolution is independent of not only the initial conditions, but also the inflationary potentials. In particular, the expansion factor can be well described by the same exact solution in all the cases considered. In contrast, in the potential dominated case such a universality is lost. It is also because of this universality that the linear perturbations are independent of the inflationary models, too, and are obtained exactly. During the transition phase, the evolution of the background is first matched to that given in other two phases, whereby the e-folds of the expansion are obtained. In this phase the perturbation modes are all oscillating, and are matched to the ones given in other phases. Considering two different sets of initial conditions, one is imposed during the contracting phase and the other is at the bounce, we calculate the Bogoliubov coefficients and find that the two sets yield the same results and all lead to particle creations at the onset of the inflation. Due to the pre-inflationary dynamics, the scalar and tensor power spectra become scale-dependent. Comparing with the Planck 2015 data, we find constraints on the total e-folds that the universe must have expanded since the bounce, in order to be consistent with current observations.