Francesca Vidotto

Towards Spinfoam Cosmology

We compute the transition amplitude between coherent quantum states of geometry peaked on homogeneous-isotropic metrics. We work in the context of pure gravity without matter, we use the holomorphic representations of loop quantum gravity and the Kaminski-Kisielowski-Lewandowski generalization of the new vertex, and work at first order in the vertex expansion, second order in the graph (multipole) expansion, and first order in volume{sup -1}. We show that the resulting amplitude is in the kernel of a differential operator whose classical limit is the canonical Hamiltonian of a Friedmann-Robertson-Walker cosmology. This result is an indication that the dynamics of loop quantum gravity defined by the new vertex reproduces the gravity part of the Friedmann equation in the appropriate limit.

Consistency of holonomy-corrected scalar, vector and tensor perturbations in Loop Quantum Cosmology

Loop Quantum Cosmology yields two kinds of quantum corrections to the effective equations of motion for cosmological perturbations. Here we focus on the holonomy kind and we study the problem of the closure of the resulting algebra of constraints. Up to now, tensor, vector and scalar perturbations were studied independently, leading to different algebras of constraints. The structures of the related algebras were imposed by the requirement of anomaly freedom. In this article we show that the algebra can be modified by a very simple quantum correction, holding for all types of perturbations. This demonstrates the consistency of the theory and shows that lessons from the study of scalar perturbations should be taken into account when studying tensor modes. The Mukhanov-Sasaki equations of motion are similarly modified by a simple term.

Stepping out of homogeneity in loop quantum cosmology

uctuations of quantum geometry near the initial singularity. We show that the dynamical structure of the model reduces to that of loop quantum cosmology in the Born-Oppenheimer approximation. This result corroborates the assumptions that ground loop cosmology, sheds light on the physical and mathematical relation between loop cosmology and full loop quantum gravity, and on the nature of the cosmological approximation. Finally, we show that the non-graph-changing Hamiltonian constraint considered in the context of algebraic quantum gravity provides a viable eective dynamics within this approximation.

Exotic singularities and spatially curved Loop Quantum Cosmology

We investigate the occurrence of various exotic spacelike singularities in the past and the future evolution of k = ± 1 Friedmann-Robertson-Walker model and loop quantum cosmology using a sufficiently general phenomenological model for the equation of state. We highlight the non-trivial role played by the intrinsic curvature for these singularities and the new physics which emerges at the Planck scale. We show that quantum gravity effects generically resolve all strong curvature singularities including big rip and big freeze singularities. The weak singularities, which include sudden and big brake singularities are ignored by quantum gravity when spatial curvature is negative, as was previously found for the spatially flat model. Interestingly, for the spatially closed model there exist cases where weak singularities may be resolved when they occur in the past evolution. The spatially closed model exhibits another novel feature. For a particular class of equation of state, this model also exhibits an additional physical branch in loop quantum cosmology, a baby universe separated from the parent branch. Our analysis generalizes previous results obtained on the resolution of strong curvature singularities in flat models to isotropic spacetimes with non-zero spatial curvature.

Cosmological constant in spinfoam cosmology

We consider a simple modification of the amplitude defining the dynamics of loop quantum gravity, corresponding to the introduction of the cosmological constant, and possibly related to the SL(2,C){sub q} extension of the theory recently considered by Fairbairn-Meusburger and Han. We show that, in the context of spinfoam cosmology, this modification yields the de Sitter cosmological solution.

Local spinfoam expansion in loop quantum cosmology

The quantum dynamics of the flat Friedmann-Lemaitre-Robertson-Walker and Bianchi I models defined by loop quantum cosmology have recently been translated into a spinfoam-like formalism. The construction is facilitated by the presence of a massless scalar field which is used as an internal clock. The implicit integration over the matter variable leads to a nonlocal spinfoam amplitude. In this paper we consider a vacuum Bianchi I universe and show that by choosing an appropriate regulator a spinfoam expansion can be obtained without selecting a clock variable and that the resulting spinfoam amplitude is local.

Evidence for Maximal Acceleration and Singularity Resolution in Covariant Loop Quantum Gravity

A simple argument indicates that covariant loop gravity (spin foam theory) predicts a maximal acceleration and hence forbids the development of curvature singularities. This supports the results obtained for cosmology and black holes using canonical methods.

Many-node/many-link spinfoam: the homogeneous and isotropic case

I compute the Lorentzian EPRL/FK/KKL spinfoam vertex amplitude at the first order for regular graphs, with an arbitrary number of links and nodes, and coherent states peaked on a homogeneous and isotropic geometry. This form of the amplitude can be applied for example to a dipole with an arbitrary number of links or to the 4-simplex given by the complete graph on five nodes. All the resulting amplitudes have the same support, independently of the graph used, in the large-j (large-volume) limit. This implies that they all yield the Friedmann equation: I show this in the presence of the cosmological constant. This result indicates that in the semiclassical limit, quantum corrections in spinfoam cosmology do not come from just refining the graph, but rather from relaxing the large-j limit.

Single particle in quantum gravity and BGS entropy of a spin network

Passerini and Severini have recently shown that the Braunstein-Ghosh-Severini (BGS) entropy S{sub {Gamma}}=-Tr[{rho}{sub {Gamma}}log{rho}{sub {Gamma}}] of a certain density matrix {rho}{sub {Gamma}} naturally associated to a graph {Gamma}, is maximized, among all graphs with a fixed number of links and nodes, by regular graphs. We ask if this result can play a role in quantum gravity, and be related to the apparent regularity of the physical geometry of space. We show that in loop quantum gravity the matrix {rho}{sub {Gamma}} is precisely the Hamiltonian operator (suitably normalized) of a nonrelativistic quantum particle interacting with the quantum gravitational field, if we restrict elementary area and volume eigenvalues to a fixed value. This operator provides a spectral characterization of the physical geometry, and can be interpreted as a state describing the spectral information about the geometry available when geometry is measured by its physical interaction with matter. It is then tempting to interpret its BGS entropy S{sub {Gamma}} as a genuine physical entropy: we discuss the appeal and the difficulties of this interpretation.

Compact phase space, cosmological constant, and discrete time

The presence of the cosmological constant can aect the quantum kinematics of gravity. Here we show that it enters naturally in loop quantum gravity (LQG) by determining the size of a compact phase space and the dimension of the corresponding nite dimensional Hilbert space. This yields the discretization of the extrinsic curvature and can be related to time discreetness. Recent results indicate that a positive cosmological constant simplies, rather than complicating, our understanding of quantum gravity. Fairbairn and Meusburger [1] and Han [2{4], building on [5, 6] and [7], have shown that the cosmological constant makes covariant LQG nite. Haggard, Han, Kami nski and Riello [8] have given a straightforward construction of the LQG dynamics in the presence of the cosmological constant, related to the geometry of constant curvature triangulations, a key idea introduced by Bahr and Dittrich [9], which grounds the present work. The LQG kinematics needs to be modied to take into account the presence of a cosmological constant; this was realised long ago by Borissov, Major and Smolin [10{12] and the problem has been recently explored in detail by Dupius, Girelli, Livine and Bonzom [13{16] for negative cosmological constant. A discretization of spacetime in terms of at simplices is not suitable for a theory with cosmological constant because at geometry solves the